A few entirely personal comments here...
I have Nikon C (clear) filters on all my Nikon lenses. I also keep a couple of Nikon UV filters for when I'm up high the the sky, like photographing in the Bromo Valley of Indonesia.
TBH, I've not noticed any differences between images made with either the Cs or the UV's in high-altitude places like Bromo.
What I do have problems with, however, is flare. With my Fuji XE2 and Fujinons, as good as those lenses are, they throw up a huge amount of flare compared to my Nikon Ds. I cope with it, sort of, by setting my exposures to -.03 or even -0.7 or -1.0 (the latter when I'm at the beach) but it's still a problem, and I find all the post-processing tricks I'm used to doing don't really deal adequately with the problem.
Next trip I take to Indonesia in June (I'm in Australia now, early winter is here and harsh lighting is no longer a problem in our dismal dark, dreary, wet days) I will be taking a couple of polarizers with me, to try to deal with this annoying and, TBH, image-affecting phenomenon.
Interestingly, on those very limited occasions when I nowadays shoot film, my Contax G (made in Japan) lenses with T coatings, all with a UV filter on them, never show these problems. Nor did my now ancient Nikkor F mount lenses on my Nikkormats in the days when I used those in place of the newer Nikon DSLRs I now prefer. IT may be of interest to some that as I used mostly Ilford B&W films in the 'mats, often I had a Nikon B&W filter on the lens, and I don't recall ever having any UV related problems with the images I did with those.
These are my thoughts, for what they may be worth to anyone.