The following is said with the understanding that my experiences are heavily biased towards the Rock\Alt\Funk\Metal type genres. And that I've now memorized 250+ songs note for note in the past 14 months.
If you're going to be in a cover band where you learn 50+ songs it's much more productive and time efficient if every single member learns each song, on their own time, near note for note.
You show up, play together and have 5-10 songs in the can. Next week you do the same thing. My belief is that the songs were recorded and performed in a certain manner and it's a nice challenge as a musician to reproduce that as well as give the crowd something familiar to hear.
When I see other cover bands I notice:
Guitar players are most guilty for just putting their "own spin" on everything. Which basically means making everything into a power chord, having a vague understanding of the rhythm and melody.
Bass players dumb everything down. Seriously guys, the songs are easy enough.

Challenge yourself some and at least learn how to lay down what's on the original recording. If you need to modify it some it's easier to afterwards.
Vocalists love to just make up lyrics, repeat verses, mix up verses. Get that stuff right. There isn't a lot of wiggle room on lyrics. Everyone in the audience is a vocalist. Not everyone is a drummer\bassist\guitarist.
Drummers tend to dumb stuff down a lot too but they are usually less guilty of this than bassists.
My overall experience when playing and auditioning for other cover bands has been that the bands that really abandon even being close to note for note are a bunch of lazy musicians. The songs tend to lack a lot of the drive and urgency that make them an individual song because it's just Rock Beat 2 with 4 chord Guitar riff 3 matched with 8th note bass line 1.
THE GOOD NEWS is there is no right way to do this. If you want to be in a band where everyone just wings it there are plenty available. If you want to be in a band where people toe the line between the two extremes a plethora of those exist. If you want to be in the almost exact recording crowd, well we got those too.
For the crowd complaining that live, bands don't even play their songs the same as recorded...they do almost always play the song the same way live from night to night.
A good compromise is learning live versions of songs.
The last thing I'll say is most cover bands perform the same songs over and over. If you've been playing a song for 6 years it shouldn't sound off when you play it; no matter if you're playing note for note or someway else.
Knowing something note for note gives you far more flexibility. You should be able to play with any band.