I have a CRT monitor that I run osu! at 140Hz (or 176Hz when I'm in the mood to drop the resolution to play osu!mania), and I've found that the high refresh rate reduces eyestrain when playing Taiko or osu!mania. It does make a difference in Standard mode (the cursor is quite a bit easier to follow, making spaced patterns somewhat easier to land), although I'm not sure about how significant the benefit really is, or how it compares to a 144Hz LCD.
But anyone who says that CRTs have terrible image quality simply hasn't seen a high-end CRT monitor, which trumps over most standard LCDs in a lot of ways. They can achieve high resolutions with great clarity (mine handles 2048x1536 if I'm willing to drop down to 75Hz, but I'd rather run a lower resolution with a higher refresh rate), generally have better contrast ratios, and natively support just about any resolution you throw at it without any blurring (low resolutions, custom resolutions, etc. as long as you don't exceed the max). And since they're discontinued, you might be able to get lucky and pick one up for a very good price (I got mine for $40 a few months ago).
The only real negatives to having a good CRT is the manual initial calibration needed, as well as the footprint on your desk and your energy bill. That, and the aspect ratio, but that's not that big of a deal IMO (I play letterboxed on some games, which I can deal with since my monitor's more than big enough. There are also widescreen CRTs that exist, and while they're the cream of the crop, they're much more rare than a high end 4:3 CRT).