That's part of the challenge!
Everything in photography has a tradeoff- film speed vs. grain, larger negative size of medium format vs. its bulk and weight, etc. Mirror lenses have limitations, but those can often be overcome.
To avoid donuts, I avoid bright background highlights. I put the sky behind the subject, or use a subdued or even-toned background. If for example the sun is glinting off water, I choose a different position to shoot from. That's not ideal, but it's usually fine. I use my Tamron 500mm a lot for distant subjects, so the background is often for me not a problem to begin with.
There are limitations compared to a refractor, but bottom line, I have the lens with me, so I get the shot I otherwise wouldn't. I would seldom carry a bulky and heavy refractor long telephoto. And I mainly wouldn't carry one because I wouldn't own one, because they're too dang expensive for me to afford.
My lens gives nice results. Yes, it's limited to one aperture, and sometimes gives busy false-detail bokeh and the aforementioned donuts. Contrast and resolution are not the equal of good refractors, but I didn't expect them to be. The images are still high quality. When shooting distant subjects (i.e. at or near infinity), atmospheric haze and heat shimmer, when present, cut resolution and contrast no matter the lens used.
I see the shortcomings as challenges, and my lens only cost $136, in great shape, in its original case with the original O/R/Y/ND-4 filters, Nikon AI and Minolta MD adapters, and the SP 2X teleconverter. A PK adapter cost another $20. For that, there's much to like, and little to complain about. I've noticed that good refractor long telephotos are rather more expensive...