I respectfully disagree with your premise as well as your conclusion. Although songs did get to be 3 ½ minutes long, it came from a number of factors, but mostly sheet music. This is all covered at length in my book (chap 3 & 4):http://dvautier.home.comcast.net/pubs/pubs.htm
It is also available on amazon.com at:
http://www.amazon.com/exec/obidos/tg/detail/-/0967704634/qid=1122519453/sr=1-1/ref=sr_1_1/002-2074593-0620046?v=glance&s=books
The player piano and its 3/1/2 minute length was a result of many things. Unfortunately I would not attribute it to the physical charastics of the player piano.
Sorry about that: