It is not just for the sake of television. This is very deliberate. Mad Men is an incredibly thoughtful (fictional) depiction of the '60s that's littered with gender and social commentary. First, you must make the distinction between classes, and age. Not every woman in Mad Men possesses these "dainty" characteristics. The first half of the 20th century required men and women of wealth and privilege to not just act a certain way, but to sound a certain way. The socially appropriate behavior of women during this time would have had a domestically reserved air. However, at the beginning of the 60's, and the first season of Mad Men, women start defying these social standards by moving to the city and maintaining jobs, giving them a role outside of the home and achieving an incredibly new social position, independence.
This hyper feminine speech that you mention does not happen with every female character however. You can see that it's more pronounced in the older or more privileged women of the show like Joan, Betty and Trudy, as opposed to Peggy and Sally. Trudy comes from wealth and therefor was raised with an emphasis in proper social etiquette. Joan realizes that to get ahead in life you must manipulate your circumstances. She uses her "feminine wiles" to her advantage, thus embracing her femininity. Betty and Trudy were raised to become housewives, that is their role in society as women. Even Joan embraces that this is something that she must achieve as a woman. They are expected to be subservient and adhere to female societal norms. That is not necessarily the case with Peggy or Sally. Peggy is rough around the edges, not as pretty as Joan and must rely on her "uncharacteristic" intelligence and determination to get ahead. She has a soft voice, but her speech would suggest that she comes from a lower social rung. Sally wasn't raised with the emphasis on etiquette and femininity because she is literally a child of the '60s. There is a sexual revolution going on and women are outwardly seeking gender equality. She wears pants, whereas the older women always don dresses and skirts. Women like Betty or Trudy, would never have been seen in pants as adolescents. And Sally has a deeper voice. Almost reminiscent of a laid back "surfer's" drawl.
This "proper" form of speech isn't only prominent in women however. Peter also has an elevated form of speech that oozes arrogance. That is indicative of his gender, but mostly of his social class. This is also noticeable in other affluent characters such as Henry Francis and Herman "Duck" Phillips. Draper doesn't seem to posses this vernacular because he wasn't a product of wealth. He worked hard (and lied) to become who he is in the series.
This behavior, of demure voices and "ditzy" femininity, enforced the ideal that women were weaker than men, a concept as old as creation myths. It is not limited to early 20th century NYC, and dates back centuries. It's good that you consider early 20th century when looking at Mad Men's portrayal of the 60's. You can't look at a single decade without looking at the road that leads up to that point. This is immediately following the baby boom. Characters still reference "the War" (which in most cases is Korea, not WWII). The 50's was a time of intense conservatism, especially in regards to the portrayal of women (perhaps in response to men taking back their jobs after WWII, and putting women back in "their places"). An example of this is Marilyn Monroe's characters in multiple films. A "sex symbol of the fifties, [she] plays … a woman-object, whose sexuality is unthreatening, guileless, and childlike" (Quart and Auster, 54). June Cleaver isn't just a character, she's meant to be an example for all women to emulate. [Here] (http://www.democraticunderground.com/discuss/duboard.php?az=view_all&address=389x5528902) is a piece of behavioral conduct literature from the 50's educating women on how to be "good wives". This type of literature has been around for centuries, and is most often written by men and displays their idea of how woman should behave.
Auster, Albert and Quart, Leonard. American Film and Society Since 1945. Connecticut: Westport, 2002.
Dixon, Penelope. Mothers and Mothering: An Annotated Feminist Bibliography. New York: Garland, 1991.
Hodges, Deborah Robertson. Etiquette: An Annotated Bibliography of Literature Published in English in the United States, 1900 through 1987. Jefferson, N.C.: McFarland, 1989.