They didn't all benefit from this and many CRTs looked like shit regardless (I recall having multiple CRTs where certain colors looked off or bled too much). Specifically, the numbers on most games (Specifically Zelda:A Link to the Past) had a tendency to bleed if the device brightness was set to anything near visible in a room during the day.

There was a device to let you play gameboy games (native LCD) on like a super nintendo or something, and they actually looked better there because of the native filtering. I'd argue the filters you can apply to gameboy games look even better now, even on LCDs.