Wait, are CRTs more color-accurate than even the best LCDs? Then again, "color fidelity" is somewhat ambiguous. I'm torn between whether that term means "color accuracy" or "color resolution".
Colour gamut is a complicated topic because there are so many different things it can involve.
The most common colour space is sRGB which was designed some time around '98 to reflect the capabilities of most CRT displays. The snag is that basically no two technologies display exactly the same colours. In LCD displays it depends mainly on the backlight, AFAIK, which can vary between manufacturers, but crucially very few LCD displays I'm aware of have perfect sRGB coverage. You end up with a situation where your display covers
most of sRGB and then a few extra bits, but any video originally encoded for sRGB is going to look a little off as the missing parts are replaced with the nearest available.
Here's a neat graphic from EIZO, a high-quality monitor company:
The wonky shape is a projection into 2D of the approximate colours most people can discern. The polygons on top represent some standard colour spaces.
You can see if you were to make something using a really strong green in the Adobe RGB space and then display it using the sRGB colour space you'd be a little sad as the green would be squished to fit in. The same thing happens in the other direction with most monitors as they don't overlap sRGB completely.
Stealing another image from EIZO, here's the normal situation:
Yellow is Adobe RGB (but it could be anything for the sake of example) and red is some hypothetical monitor. You can see there's a ton of colour the monitor can show that no ARGB image is going to include, but more crucially a lot of the very saturated colours are going to be just a bit off because they have to be crushed into that funky polygon on the right.
Trying to make colours work nicely is an unending game of trying to make more, bigger, triangles (or sometimes quads! especially in printing) and write software that correctly translates colours between them. You can read the whole EIZO article here, I don't know if it talks about everything I did because I'm a massive colour theory nerd but it covers a lot:
https://www.eizo.be/en/knowledge/monitor-expertise/understanding-color-gamut/I also made a quick example of my personal hell with colour gamuts, converting between sRGB and CMYK for printing:
See how the green at the bottom on the right one is darker? That's because CMYK doesn't go as far into the saturated green corner as sRGB. All the old films and stuff are suffering from a similar problem, just... all digital.
TL;DR a limited number of colours are stored and a limited number can be reproduced and most LCD monitors don't have exactly the same colours as used to be standard on CRTs so a lossy conversion has to be made.