People who are into older games tend to have a CRT + retro rig or digital to analog converter. A lot of older PC games legitimately look nicer on CRTs. Additionally, CRTs can have ludicrously high refresh rates and resolutions, don't let the 4:3 aspect ratio fool you. High-end CRTs (specifically computer monitors, not TVs) tended to max out at 1600x1200 (vs 1920x1080), giving them a slightly larger vertical resolution at the cost of a lower horizontal resolution, with some going as high as 2048x1536 (comparable to 1440p (yes, 1440p, CRT computer monitors were mostly progressive scan, not interlaced like TVs)). Additionally, the refresh rates on later CRTs tended to start at 75hz (vs 60hz on LCDs), and could max out at 200hz on high-end monitors. You'd sacrifice resolution to do so, though I think you could mitigate some of that by using a BNC cable if your monitor supported it (though I doubt most rigs could run anything even close to 200fps without decreasing resolution). Finally, CRTs tend to have extremely low response times, very good color depth, and true blacks.

That said, CRTs are heavy, fragile, and nowadays, expensive (before the pandemic you could get a high-end Sony Trinitron 20" PVM (professional video monitor) for like, $300-$400; shipping was more expensive than the monitor, nowadays you're easily talking $1000 or more). Most LCD panels can beat CRTs in resolution and refresh rate nowadays (though even high-end LCD panels tend to struggle at beating CRT response time), and OLEDs outclass CRTs in almost every way.

Edit: oh, another weakness of CRTs is that they can burn-in. That's where the term originated. If you left an image on the screen too long, it'd burn into the display, causing it to persist even after the monitor was turned off and unplugged. Since no one's making CRTs anymore, that means there's a smaller and smaller pool of CRTs in good condition, which means they'll get more expensive until someone decides it's worth the money to start making the tubes again.

Edit 2: that's also why screensavers were a thing! Screensavers were there to stop you from accidently burning in your monitor. I wonder why they haven't made a comeback with OLEDs.