This 3 ½ pop song time is an interesting discussion and to tell the truth I never thought about it very much. 3 ½ minutes was the time that Stephen Foster began using but I’m not sure why. Some of it I suppose had to do with the standard number of pages that sheet music used around that time. This was for manufacturing and and paper considerations. There is also something about the human ability to focus, or maybe a desire to make his music distinct from classical which was always longer. He wanted people to dance to his music and 3 ½ minutes was a good time to use.Minstrelsy and vaudeville established a similar venue, the first because of the great Foster influence, the second perhaps because it suited the fast-paced playbills of vaudeville.
A notable exception to the 3 ½ rule came during the 1890s when waltzes became the rage. Even though today they are between 3 and 4 minutes, remember waltzes were played at that time at 30 beats per minute so people could actually dance to them. Today Daisy Bell is played at an astonishing 40 to 50 per minute.
The record and player piano manufacturers followed suit as you suggested.
It was not until the Beatles that the 3 ½ rule was seriously challenged. Many other artists followed.