Back in the day when you could be in a band and play 2 to 5 times a week and get paid well, bands used to learn a good amount of their material very close to the record.
Now the pay is so low, and bands don't stay together very long usually,it has gone to trash and bash quick and dirty lets do the easy songs that everyone knows type deal.
I still like to learn a few tunes here and there note for note,if the drum part is really cool,or challenging/creative,and with my cover band I try and learn some fills in songs esp if they are signature fills or really a big fill make it obvious to the band (and audience) when a middle eight, bridge, pre chourus ,is approaching or ending.
If you are in a cover/copy band I think it is important to have the skill/ear to learn a song note for note if needed,and it is a good skill to have if you get into a serous/pro cover,variety or tribute where you can make good money and get booked a lot.