Good drummers don't need a click, bad drummers can't play to a click. Make the choice
If you want to add more layers to the music, extra guitar tracks, more synths, backing tracks, then recording with click is mandatory. Yeah, maybe you can fix it afterwards in the DAW, I've done that with some recordings, it takes friggin' FOREVER! Don't make life unnecessarily harder for yourself then it has to be. And if the band still refuses, charge them for your time fixing their mistakes.
Playing clickless doesn't exclude adding midi stuff, even without nailing everything to grid, which can be a huge chore and mess up the song or feel completely. I only use Reaper so I speak for that program, but it's a quite easy process to find the true tempo of the performance for each and every bar separately. Then you have a song that's in click, or rather a click that's in the song, and the grid conforms to the performance. I use this in our current album project, which is sort of "roots" music, no need to quantize everything into techno music. But since the song is "in click", it's easier to do midi edits and add stuff.
And then it's also fun to point and mock the drummer: "Look here you speed up by 3bpm!"
Good drummers don't need a click, bad drummers can't play to a click. Make the choice
And to those that say find new musicians to play with, these are my best friends basically.
I wonder how the Beatles recorded so much w/all the tempo changes and no click? Oh, that's right, it's been said that Ringo was a human metronome...
Ton of good old songs have 'variable tempo' but I find a click detrimental for looping, cutting, copying, etc. There are work arounds. Some musicians feel like a 'click' track is judge and jury. I have one awesome client that despises them. So I pick a simple drum loop he likes and drag it out and he's good.
So there are optional MIDI instruments in a project such as tambourine, maracas, hi-hat, etc. that can be substituted. Alternately, if you use Logic, you can flex time the drums after the take however it would be a fairly brutal task for multi-track drum take.
And to those that say find new musicians to play with, these are my best friends basically.
I'm not sure that recommending the guy quit the band with his best friends over the question of a click track is appropriate. Being in a band is about compromise. Try it with, try it without, then have some beers and talk it over.