My opinion??as a very analytical person I have to disagree. If we are not playing in time, especially on the covers, then we will sound really bad. A lot can be said for feel and energy in songs, but starting a song at 90 bpm and ending it at 120 bpm is never a good thing. (unless it has intentional tempo changes)
I thinke we will sound much better without: bass lines that are supposed to be syncopated 16th notes that comes out sounding more like a bad attempt at triplets, or hits not syncing up, or rests that last a 16th note too long, dragging, rushing, etc.
You are WAY over-thinking!! You're spending so much time on these technical aspects you're making music a JOB!! This is MUSIC man!! FIRST, it's supposed to be FUN, and FEEL GOOD, (even when you're getting paid)!! THEN you make the necessary changes to make the minutia perfect.