Kronbit's PixaTool is a powerful image/video processor that can pixelate and apply palette on the fly, but more importantly you can tweak several settings to get the best out of the palette for each texture/visual/etc.
The main page is quite explicit about its capabilities: https://kronbits.itch.io/pixatool
A demo is also available.
I had a quick test the other day with the skin texture for Quake's Ranger:
You can see the improvement between the middle and bottom skins.
If only we had such a tool 15 years ago..!
