Very interesting thread. First, let me say I sympathize with both sides, since I've been a gigging musician (on both bass and guitar) for over 30 years, and I'm also a studio rat, having made my living as an engineer for many years as well.
The sound in a live venue or on a recording is a collaboration between the musicians and the sound man, and it takes both sides doing their job well, and working together, for the final product to be the best it can be.
As a player, it's all about context. Whether in the studio or on stage, the sound that works best in the context of the band often sounds pretty crappy on its own, and I highly advise folks to record their gigs, and hear what they really sound like with the band. In most of the places I play these days, most of my sound comes from my rig on the stage. I've done this long enough to know that I have to change my EQ a bit for every place we play. The vast majority of clubs are pretty poor acoustic environments.
As an engineer, you have two bosses. Your job is to help the musicians realize their vision, but you also have to satisfy the folks paying the bills (the club owner, record label, etc. is paying for a certain sound).
If it's an experienced, professional band, you can probably just take your cues from them. A friend of mine, who is a great engineer with many platinum record credits to his name, told me about one of the first sessions he ever did. He was still a teenager, and found himself behind the console in the studio with Jaco on the other side of the glass. My friend is getting things together and Jaco is ready to record, so he asks what the holdup was. My friend told him "Just a minute - I'm getting my sound." Jaco's reply was "I'm F'in' Jaco! It's MY f'in' sound - you just have to hit record!"
If you're working with less experienced folks, or if you know the room's deficiencies really well and the band doesn't, you may have more work to do to tailor their sound. And try telling the bass player "I know you can't hear it on stage, but there's this terrible standing wave at 80 Hz in this place. If you can trim some of your low end, you'll get a lot more definition, and I promise you the bass will still be powerful out front." We're often reasonable people!
And sound men, for goodness sakes, walk around the club and listen from more than one vantage point! I love the control of the studio, so I never did a ton of live mixing, but every now and then, a band that I had recorded would ask me to mix a showcase gig for them. I mixed a show at a club that was pretty famous for big reggae acts, and the sound system always had this huge, pillowy, muddy bass, that worked for that stuff, but was horrible for other music (I saw the Chili Peppers there once, and you heard from Flea was rumble). I vowed I would get a good mix that night, and it was easy to get the low end sounding great, so I wondered what the problem was for these other sound guys. Then I stepped off the mixing platform to walk around the room, and as soon as I did, I got hit with the giant muddy rumble. I spent the next 10 minutes hopping on and off the riser, and was able to dial it in, but for all the shows I saw at that club, had nobody ever stepped off the riser?!
The sound man also has to understand the system. I'm not saying that's the issue with the OP, but a lot of today's systems have way too much power and way too many subs. That's fine for that annoying "slam you in the chest" kick drum that's popular in a lot of music, but it's just wrong for a lot of other music. I saw a triple bill at BB King's in NYC a while back. The first act was Bob Brotzman - killer solo acoustic slide player, who does some percussion stuff on the guitar as well. Every time he hit the guitar, the audience was just crushed with the thump. Next act - the Campbell Brothers - sacred steel based gospel funk/blues. Again, we're just getting killed with low end. I walk around the place to make sure it's not just where I'm sitting, and no, it's everywhere. The 3rd act is Sonny Landreth, and I had just helped record his live record. I didn't want to have a confrontation with the sound guy, but I really wasn't going to enjoy the show with the low end the way it was, so bracing for a battle, I went up to talk to him. As it turned out, I didn't have to give the guy any of my background, or fight about why he should listen to me - the guy was very open. Way better mix for that set.
As an engineer, I've worked with folks who had their acts totally together, and I've worked with folks who needed a lot of coaching. Approached correctly, most folks are pretty open to that. As a player, I've had awesome sound men (the guy at the big outdoor gig going up to every single box and putting a little piece of tape on it. I ask what he's doing and he tells me he's checking the phase on each one and doesn't want to miss any!) and some lousy ones (the guy who "fell asleep" at the board comes to mind). It definitely works best when the band and the sound guy are both good and on the same page.