How many people on the average bus or train are listening to music? And if you see someone driving a car, how likely are they to be listening to music? When you go to a bar or club, how often do you hear music? When you see an advertisement on TV, how often is it accompanied by music?

Nowadays, there are a ton of different ways to hear music. Before recorded music became widespread, there was only one way: to have a musician within earshot. And since most people didn't have the money to hire a musician to play for them all the time, they had to make their own music.

I'll focus on Ireland for a bit, since it's an area I'm familiar with. You'll find tons of anecdotal references similar to Pepys' diary referring to singing.

Musician Terry Teahan's recollections from the early 20th century:

There was always singing. There was hardly not any night when somebody was not singing. I remember when I was six not being allowed to stay up to listen to it, but by the time I was eight I went to the close-by homes in the section. At home in my ma's time they were always accompanied by a flute or a fiddle or a concertina. Each one took a turn singing. It was easier to get the womenfolk to sing that it was the men.

Musician and traditional music collector Francis O'Neill, also around the turn of the 20th century:

AS CROFTON CROKER says, the Irishman, like the Frenchman, sings his conquests, his prosperity, his defeats, even his miseries and misfortunes. Conquering or conquered, in plenty or want, happy or distressed, sorrowful or gay, he always sings. To this disposition we may attribute our treasures of melody and our bewildering plenitude of song.

It's also worth noting that so-called "broadside ballads" sold quite well before the advent of recorded music. They were cheaply printed sheets with the lyrics of newly composed ballads on them. They often didn't have the music written out; instead, they might give a well-known tune that fit the notes well. O'Neill notes that

Any traditional air suitable to the metre of a new song was liable to be pressed into service; so that in course of time many songs were sung to the same air, thereby confusing its origin and history.

Now, people wouldn't be buying these if they didn't have the intention of singing them, and the sellers would advertise by singing their selections on the streets. Ben Franklin did this for a time in America, saying in his autobiography

I now took a fancy to poetry, and made some little pieces; my brother, thinking it might turn to account, encouraged me, and put me on composing occasional ballads. One was called The Lighthouse Tragedy, and contained an account of the drowning of Captain Worthilake, with his two daughters: the other was a sailor's song, on the taking of Teach (or Blackbeard) the pirate. They were wretched stuff, in the Grub-street-ballad style; and when they were printed he sent me about the town to sell them. The first sold wonderfully, the event being recent, having made a great noise. This flattered my vanity; but my father discouraged me by ridiculing my performances, and telling me verse-makers were generally beggars.

Going beyond Ireland, it's worth noting that the melody to the American national anthem is based off that of a song from a club that celebrated the mixing of wine and music, the Anacreontic Society. This is far from the only social club that featured singing heavily, and Pepys himself notes the social aspects of singing a lot, as you have read. Here's another mention:

Here I met with Mr. Lock and Pursell, Masters of Music, and with them to the Coffee House, into a room next the water, by ourselves, where we spent an hour or two till Captain Taylor came to us, who told us, that the House had voted the gates of the City to be made up again, and the members of the City that are in prison to be set at liberty; and that Sir G. Booth’s case be brought into the House to-morrow. Here we had variety of brave Italian and Spanish songs, and a canon for eight voices, which Mr. Lock had lately made on these words: “Domine salvum fac Regem,” an admirable thing.

And in Germany in the 19th century, Brahms based his Academic Festival Overture on popular songs sung by university students in social situations, many of which involved copious amounts of alcohol (some things don't change). Again, think of all the social situations that involve music now. They would have had music back then, too, but they'd have to make it themselves.

One final piece I'll tell you about are the Irish Travellers, who up until recently were an itinerant group who travelled around Ireland doing various jobs, including busking (playing music on the streets). I did my master's dissertation on singing in their community, including an audio documentary,, and touched on the decline of traditional singing in that particular community. I don't want to get too far into my own research for fear of violating the "you are not a source" part of the rules, but I will quote my own dissertation on this particular subject, if the mods will allow it:

Music and work went hand in hand for many tinsmiths. Munnelly tells the story of Pat Ward of Longford, who would similarly listen to music and sing along while working:

He tells me that he ‘can't help it,’ and he could not refrain from accompanying his hammer even if he tried. I have been told on a number of occasions that the majority of tinsmiths had this habit which helped to keep the songs fresh in their mind. (Munnelly 1975)

James continues to listen to music while working, which he now does in a small shed behind his house. Martin tells me that he does works “near enough all day, every day,” and that his music is on constantly, a fact evidenced by the large stereo system and collection of CDs in the shed. While he no longer has a campfire to work around, it is obvious that James is not only trying to preserve his craft, but the environment within which he learned it.

The Munnelly reference is to Tom Munnelly's article "The Singing Tradition of Irish Travellers," available on JStor if you have access.

Unfortunately, most of what we have to go on about the decline of singing is similarly anecdotal, but the pattern always involves recorded music replacing the act of making the music, whether it's through the radio, records, or now with the ubiquity of smartphones and mp3s. It's worth noting that both Teahan and O'Neill were writing about a time when recorded music was around but fairly new. Many, especially in rural or poorer areas, didn't have access to the recordings, and those who did would still only have had a limited collection. So there was still room to make your own music, but advances in technology and the advent of broadcast media brought more and more recorded music to more and more people.

I could go on about work songs, which were hugely important in many areas where coordinated efforts were needed (music helps keep everyone in time), or about the one space where participatory music still reigns, churches, but I'll stop there.

TLDR; There was a lot more singing and music making by amateurs back in the day, and a lot more live music than we are accustomed to now.

EDIT: Added a few more points about social singing situations.