I believe there is black, white, and grey to this issue.
The black and white. 99% of the time if you're auditioning for a band, whether it be covers or original, you're most likely to land the gig if you nail the material note for note and can play it flawlessly. That's been my experience as I seem to more often than not be the only guy who DOES nail the material, and the bands that offer me the gigs tell me so. Happily. And I've heard TONS of negativity regarding bassists who've come down to auditions, not knowing the material. It's usually accompanied by, "what the hell are these guys thinking?"
Also black and white - you nail Won't Get Fooled again note for note, you gain lots of points against the guy or gal that's improvising all over it. Same for lots and lots of other songs. I'd give more examples, but it's 6AM. Also, if it's a tribute band then don't even think about playing your own thing.
The grey - if you're an original band throwing some covers in, then by all means do it your own way. If you're doing Zeppelin, any jam band, funk stuff, etc. then the idea of playing note for note gets kind of ridiculous. But unless the entire band is truly making the songs their own, then the improvising IMO needs be left to a minimum, and the jams are only parts I myself will go off on.
Only time I won't work on nailing established material note for note is when time doesn't allow, and I have to use cheat sheets or whatever.
I absolutely don't believe it cramps anyone's creativity, or limits it. I think that's just a copout for not wanting to, or not being able to learn note for note. I can go off playing covers in my house being insanely creative and playing all over the place, I can write my own material, there are lots of times and places I can express and expand my creativity. Butchering somebody else's work I don't think is the proper place. And I disagree with the, "if I want to hear it note for note" I"ll listen to the radio camp. For the most part, note for note is what people want to hear when they're listening to covers. Only a rare musician here and there will complain regarding hearing things note for note. I can't see many in the audience ever saying, "This band sucks. They sound exactly like the recordings. I'm leaving!" Nope, it doesn't happen. Quite the opposite in fact.