I am an electrical engineer specializing in RF transmission and radio. The problem with bass tones may have been in the speakers of the receiving radio unit; it was certainly not in the transmission.
Human hearing has an audio frequency range of 20 Hz (very low) to 20,000 Hz (20 kHz, very high). Most people over 40 have lost the upper end of this range. Once you're not a teenager any more, your hearing starts to attenuate above about 10kHz. Teenagers used to take advantage of this change to use their cell phones in class, setting their ringtones to a very high "mosquito tone" in the 15 to 20kHz range. They could hear it, the older teacher couldn't.
This honestly does not matter much, because almost all vocal information in human speech encodes entirely in the lower frequency bands. Some quick internet research confirms that the primary frequency data in human speech is in the 50 to 500 Hz range. The range we are taught in school is up to 5kHz, to catch and encode harmonics generated in this range.
Amplitude Modulated (AM) radio transmission was discovered/invented in the late 1800s, and was in wide commercial use by around 1920. It's still in use today, using carrier frequencies of 550 to 1720 kHz. Commercial AM encodes audio frequencies up to 5kHz, which is fine for speech, but not so good for music. Music, especially classical, uses the whole frequency range of human hearing, encoding information and harmonics up to 20kHz and beyond. That's why almost all AM radio is speech-based talk radio, and music on AM stations tends to sound flat - the lively upper frequency band has been entirely removed.
Another place you run into technical restriction of voice band transmission is on the telephone. Plain old telephone service, called POTS for short, encodes 300 - 3300 Hz and cuts off the rest. This is why hold music often sounds so awful - it's missing both the bass, and the high end. There has traditionally been an industry producing special music used specifically for telephone transmission as hold music etc - that's why a large company may have hold music that doesn't suck so bad, but a small company, trying to use some MP3 they loaded onto their call manager as hold music, sounds like tin-plated death. Your cell phone, encoding voice as a digital data stream instead of old-fashioned analog, can capture and transmit much more data - my Samsung Galaxy Note 8 has a little "HD" phone symbol it uses to show me that it's sending higher fidelity audio, something like 50 Hz - 15 kHz, to a similarly-equipped digital handset on the other end.
AM Radio was first onto the scene because it's technically easy to do. Building an AM radio receiver is a standard first electronics project for kids as young as 8 years old. A transmitter needs more power, but is also fairly simple. Frequency modulation, FM, is technically more difficult, but like many things in engineering, has some payback for the difficulty. Using FM, you can smash more information into the same amount of RF spectrum. Commercial FM encodes audio up to 15 kHz, which makes it much more suited to music. That's why so much music is on the FM dial of your radio.
All of this means, in short, that transmitting the lower bass band of human speech is not so hard. Transmitting the upper band is more difficult, but usually unnecessary. The real challange with bass is in reproduction. Lower frequency sounds needs a larger speaker - lower frequency means longer wavelength, and longer wavelength means physically larger structures. The wavelength of a sound wave is equal to the speed of sound divided by the frequency - so a 20 Hz sound needs a 16m speaker for full-wave reproduction, but a 3.3kHz sound needs a 10cm speaker. This relates to the huge speakers you see as bass drivers at a concert. Fortunately there are some tricks we can play to get good low tones out of smaller speakers, or your home stereo would be enormous. It also explains why you can always hear your neighbor's bass line just fine through the wall. A 4-inch thick wall can attenuate most of a short wave, but a big long bass wavefront does not even notice the obstacle.
There may have been, almost certainly is, some socio-culteral reason for the use of a specific accent on a nationwide broadcast system. There is not any technical reason for it.
I studied linguistics in undergrad and specialized in historical and sociolinguistics. The Transatlantic or Mid-Atlantic accent is called such because it sounds like it’s located in some geographic point between the US and the UK, having a blend of features from both dialects. However, it was used only amongst Americans (and some Canadians), and linguists generally agree that the Mid-Atlantic accent is not a native accent but an affected or cultivated one.
The study of affected or cultivated speech falls under the field of sociolinguistics, which is primarily concerned with the social and cultural implications of speech patterns. A persons speech can be "affected" when an affinity for a certain group, locality, or culture causes them to emulate the supposed speech patterns of its people. One easy (and generally negatively viewed) example would be the middle-class white boy who adopts, and sometimes incorrectly applies, aspects of African-American Vernacular English, because of the cultural associations made with this speech (his favorite rappers, etc).
From the late 19th century to about the 1950s, the culture and speech of the English gentry was the emulated standard for elite and educated Americans. A literary example of the preeminence of the values of European aristocracy in the American upper-class is The Age of Innocence by Edith Wharton, published in 1920 and set in 1870s New York. The characters are wholly obsessed with the status that can be conferred upon them by their associations with European aristocracy, and one character's attempts to be divorced from a European count cause a polite social crisis amongst her family.
The specific speech pattern of English gentry that Americans came to emulate was Received Pronunciation (RP, or the Queen's English), which is considered the elite standard for British English to this day. One notable feature of this dialect is that it's non-rhotic (r-less), so the word car (kɑr in American IPA) is pronounced cahh (kɑː in British IPA). This might be the most recognizable feature of Mid-Atlantic English and stands out because American English is rhotic - think of the wealthy woman in a film noir who says dahhling for darling.
Mid-Atlantic English was taught to upper-class Americans by their private tutors, etiquette teachers, and cotillion coaches and was reinforced amongst the wealthy for its perceived likeness to RP. This was also at a time when the Eastern US was much more linguistically diverse than it is now - Boston, New York, Philadelphia, and Baltimore each had wildly distinct local dialects, and Mid-Atlantic speech unified the upper classes of these cities with one dialect.
Mid-Atlantic speech was further reinforced by the development and dissemination of talking films. Film studios began training actors to use it in film, and it brought with it all of the well-established cultural associations of RP. Many of these actors started using it in public life as well - notably Bette Davis and Katharine Hepburn. Its rapid expansion in American culture probably also lead to its decline, as it was no longer the exclusive realm of the elite and even began to be satirized in some media.
The Mid-Atlantic accent is so well-known because of its use in film and amongst Hollywood stars, however there are many examples of affected speech in other languages as well. In France, young educated people who aren't from Paris might try to emulate the metropolitan region's speech. A different example in English would be Cultivated Australian English, which similarly emulates British RP, and can be heard by well-known Australians like Cate Blanchett. Overall, a cultivated accent is when a larger group uses affected speech to the point when it becomes its own established accent or dialect that is still markedly different from its target dialect.
Generally, the standard accent of a country's main language will defer to the main hub of political, social, and economic power. In many cases, this is also related to whichever race holds said power.
The standard accent will often stem from one of the main cities of the country which is usually the home of that country's political, economic, and therefore social hub e.g. Paris. In Britain, the 'proper' or posh accent is the RP English accent (although, strangely, this isn't the same accent as the Queen's). This is where the social and economic factor comes into play whereby more rural accents or accents of people who do not live close to the national hubs are seen as either improper, odd, or sources of humor. This can be seen in the discrimination when it comes to lower/working class accents even if the accents take place in the national hub e.g. London.
In South Africa, the language of Afrikaans developed within the last four hundred years. Initially, it was a unifying language among slaves and slave owners and drew influence from a variety of languages with Dutch being the 'base' language. When Afrikaans pride by the White Afrikaans people flared up during the first Anglo Boer war in the 1800s, Afrikaans was claimed as the language of 'proper' South Africans i.e. White Afrikaans-speaking people. This 'Afrikaner Pride' continued and Afrikaans was the language of the National Party that established and ruled during Apartheid. Much of the wealth and all of the political power in South Africa was held by white Afrikaans people and thus it became the national standard to which South Africans were expected to defer. The way in which people of color and poorer communities spoke Afrikaans was deemed as incorrect and mocked or viewed as a sign of lower intelligence even though it is from those communities that the language developed in the first place. Ironically, there has been a shift of attitude towards Afrikaans as people attempt to distance themselves from the Apartheid era whereby the ability to speak English is seen to have some sort of higher social status, especially if the accent with which English is spoken is close to that of the white English South Africans who settled in SA in the 1800s. They were the formidable opponents to the Afrikaans people in colonizing South Africa as their own and set off the call to action by Afrikaans people to establish themselves and their culture. Currently, British English and American English are viewed as 'posh' and indicators of a higher social status regardless of the socio-economic status of the accent within the region from which it originates.
America is rather unique in that the General American accent stems from the exact opposite reasoning around deferring to the national hub. There are theories that the Midwestern accent became the General American accent due to subtle racism and xenophobia. When the General American accent developed, there was a strong influx of immigration in one of the country's biggest hubs, New York City. The expectation would be that because of the massive influence New York City had on the country, the New York City accents (or a generalized version thereof) would become the societal standard. However, attitudes at the time looked towards the rural (read Midwestern) population as the 'true' Americans who were there from the beginning i.e. about 300 years prior. This was in no small part due to the fact that there was minimal immigration further inland and that the Midwestern populations were largely White. The rise of the GA accent coincided with both the development of radio and the influence of the Trans Atlantic accent. The two accents were meant to be devoid of regional inflection, yet distinctly American. Funny enough, the idea of the General American accent doesn't ring true in practice as there are a variety of accents that exist in the Midwest.
The belief in a General American accent being related to whiteness can be seen when challenged in media and studies whereby African Americans adopt a 'White' (read General American aka Midwest) accent in order to avoid prejudice and stereotypes. The opposite can be seen whereby POCs in Hollywood have to often put on an accent that relates to their race for comedic value. My favorite example of this racial prejudice with accents is when The Daily Show with Trevor Noah was berated for forcing one of their correspondents, Ronny Chieng, to put on an offensive 'Chinese' accent, but it was revealed that the accent was Chieng's actual accent when speaking English.
The standard accent of a language is largely related to who holds power. This is very often related to the way in which middle and upper-class members of society speak that language and the existence of those classes relate historically to race.