Sure, change the song, IF, EVERYONE agrees that you aren't gonna play it like the studio version (maybe incorporate the live version, or stretch out the guitar solo). However, some just don't want to take the time and actually play the changes different. My experience is if everyone has a recording of the song it makes it so much easier to get tight. Band practice is for working on endings and vocal harmonies, not for learning the song.
Something else I've noticed lately, is that singers are taking lessons to learn songs exactly the way they're done on the recording. A lot of vocal teachers use the backing track to show land-marks for singers in the song. If you change those things the singer can actually be thrown off and lose their harmonic center fairly quickly. It'd probably not be as big a deal for rock music or some of the fast stuff but for ballads you usually have to be bang on or the singers have a heck of a time.
...and you just don't want to mess around with a singer who does ballads... or it'll be your last gig with them...
But back to the topic... sure sheet music is a "crutch" I'll give you that... but it's required if the band is playing something they've never seen or heard before - which is pretty common in modern music.