i agree with both sides of the "i need to feel good on stage" discussion. on one hand, the tone and guitar has to inspire the player to play well. on the other hand, the audience probably can't tell the difference between certain effects or tones. i know non-musicians who literally can't discern a clean guitar from a distortion guitar, honestly. "it sounds like a guitar to me" is what they say. so forget about mesa vs marshall.
but i think there is a "danger" of being too meticulous about things as well. i know musicians who literally "can't play guitar" when something very small is not how they want it. something like less than 1dB of a frequency being off in the guitar tone, or reverb mix not being EXACTLY perfect, etc etc. there's a well-known player here who brings a tech with him even for very casual gigs (like restaurants, background music gigs, etc) and during the performance he has specific hand signals for specific adjustments. during the gig he may be signaling like crazy while singing and playing to adjust things that even i have trouble discerning if anything changed. like.... .2 dB more of 600hz, or -.4 of 400hz, etc.
and hey, if he needs this stuff, that's all cool. but it kinda really detracts from the performance. maybe his ears have evolved so much more than mine, and again that's great and cool. i also have definitely been in situations where the stage is just sooooo bad, like a crazy honk around 400hz (i HATE 400 actually haha) and yeah it's super challenging, or feeding back and it just needs to be fixed. but that's a bit extreme and pretty obvious. but flailing hands, which means stopping guitar playing, while singing a song just has a strange look on stage... all gig long. maybe that's just me.
i've always strived to just play the gig and present a good performance. i try to adjust the sound as best as possible, but at some point you have to play and connect with the song, and if appropriate, connect with the audience as well. if something is so catastrophic, i let the management know that i need time to fix it, and usually they're like "oh yeah everyone sounds bad here, is this why?" and i explain just a bit so we're on the same page.
feeling inspired is super important for sure. but i try not to let the small things get in the way if possible. it's a gig. it's over in 3 hours. and most people won't know or remember what happened anyway if it's something small that can't be discerned by most. get inspired of course, but sometimes you just have to play the gig.