I work with a professional composer/music director/performer who always brings his own instruments. He played those exact instruments for years, and knows which one(s) will work best for what he wants to accomplish, the space he'll be performing in, and will play nice with our sound equipment. While he has occasionally asked us to have a back-up guitar on site, just in case, I think he'd be insulted if we asked him to play something other than his own.
I believe he carries his own insurance for his instruments, since they're part of his livelihood (and as someone who used to play an expensive instrument, I'd recommend that for all musicians!) which still covers them in all performance venues.
We do provide plenty of his preferred type of strings (one set per week of performance, but we do 13 shows a week), batteries for anything he needs them for, sound cables, DI boxes, contact cleaning supplies, etc.
Thinking back on all the shows I've done where performers play an instrument, the only instruments my theater has ever provided are a keyboard, and small hand percussion, whizz whistles, kazoos, etc. (though there was one performer who preferred his personal kazoo!)