This is a big issue with demanding gamers like those in the speedrunning community, a traditional (15KHz) CRT is a must for low latency.
The concern for CRT loss was valid, however things are finally starting to look a bit better..
I'll guess I will go a bit technical since I work with & troubleshoot "old system video stuff" quite often..
What old consoles / arcade games pretty much always used was RGB input, which was virtually artifact free. Although with consoles you usually had to resort to composite/RF/svideo, RGB being more common only in EU/JP regions. NTSC/PAL artifacts also can still be included easily with an otherwise superior image, but I won't get in to that here..
Biggest issue with flatscreens has always been that they only handle native resolution, anything else than native has to be scaled to be that specific resolution, resulting in blur and loss of image quality.
What's even worse, older systems and games sort of hacked around the typical broadcast standards where it kept transmitting one field instead of alternating between odd/even, this gave you a stable picture of 60fps (Closer to 59.94Hz in reality) with the expense of dark lines on every other scanline and only 240 lines of vertical resolution. "Stretching" of the image happened naturally as the lines for both fields would go from top to bottom, resulting in a crisp image that was rather flicker free.
Unfortunately almost no scaler that has been built actually respects this hack, hardwired to expect both fields, which is a 480 line image. While this works for TV broadcasts and looks quite good with such, it has very varying results with older systems as the flat panel will attempt to treat this low resolution image as something that's supposed to be higher resolution, resulting in awful scaling artifacts or the whole picture jumping/flickering.
However there are thankfully scalers out there that do, like the micomsoft xrgb series or a pure linedoubler like the earlier xrgb or ther more recent ossc.
With these, you can get pretty darn accurate results and can even simulate scanlines.
While CRTs look cool, they're not all so cool to work with.. they can get dark/blurry/get color offset even after a couple years of active use on some cabs. Not saying they all do but rarely do I see a crisp image on an arcade cab crt these days. Flat panels do have their own issues but I guess what I want to say here is that It is indeed getting harder and harder to find replacements for a reasonable price, unlike flatscreens where an older 1600x1200 panel from 10 years ago can be perfect.
Now I hate to sound like an advertisement but I highly recommend checking out the OSSC, It's a no compromise solution that does pure linedoubling, very good digitizing that keeps colors intact (along with noise filtering) and allows you to keep the original refresh rate intact, all combined are something that no scaler does. Personal results with flat panels and say.. a megadrive has given me pretty much emulator crispness on the picture and virtually zero latency (we are talking about a few scanlines as it doesn't have a framebuffer).
Anyway, tools are there to get a superb image out of older systems, including consoles that have RGB output available.
I wouldn't worry too much anymore as the quality you can get has already surpassed a CRT.
Currently the main problem is the entry price, which can cost you $200 or up.
Most likely in the future stuff like this is gonna come down in price and re-implemented & cloned for cheap in china.
Cheap scalers that do better than the average TV do exist but I'd say that they still fall short.