The songs that become most popular are the ones played on broadcast commercial radio. There is a new trend towards other delivery mediums such as sirius xm and YouTube but for decades broadcast radio was where "hits" were born.
The reason for the existence of broadcast commercial radio (like television) is not to provide a public service or play music or bring you news, but to sell advertising! The more listeners a station can retain at a given point in time, the more money they can charge for their ads and the more profitable the radio station as a business becomes.
In order to attract the most possible listeners, program directors recognize that they need a wide variety of content. If they only play 5 songs in an hour, the station is less likely to play something a particular listener likes than if they can play 12 songs in an hour.
If the songs are 3 minutes long, the station can play 5 songs in 15 minutes and then have 5 minutes of commercials and then do it again. By playing 5 songs in a 15 minute span instead of two, a given listener is more likely to hear something they like and stay tuned for the next set in case they might hear something else they like. And if they don't like a particular song, they know they only have to listen for 3 minutes and anyone can wait 3 minutes. If they did not like the song and it was a 7 minute song, they are more likely to turn the dial (change the channel).
So the 3 minute rule became an accepted formula among radio station program directors. The "radio cut" of longer songs, shortened them into this radio friendly length.
Bottom line, if you write a song in hopes that it may get airplay on commercial radio, try to keep it in the 3 minute mark.