As far as I know, 3 minutes is the standard time slot for radio play, and a song that's longer than that will be more difficult for DJs to schedule and thus will get less air time. Thus, musicians try to fit their songs into that time slot to maximize royalty revenues.
This doesn't seem to come from any physical constraints of old media, since a 7-inch 45 RPM record (the standard "single") had a recording capacity of about 5 minutes per side.[1]
Billy Joel, in his song "The Entertainer" (1974), has the following lines: [2]
I am the entertainer
I come to do my show
You've heard my latest record
It's been on the radio
Ah, it took me years to write it
They were the best years of my life
It was a beautiful song
But it ran too long
If you're gonna have a hit
You gotta make it fit
So they cut it down to 3:05
Wikipedia says that this "references the shortening of Joel's song, 'Piano Man', from 5 minutes and 38 seconds to 3 minutes and 5 seconds to fit a radio slot".[3]
[1] http://history-of-rock.com/record_formats.htm
[2] http://www.metrolyrics.com/entertainer-lyrics-billy-joel.htm...
[3] https://en.wikipedia.org/wiki/The_Entertainer_(song)