Most older LCD TVs do not have either black frame insertion or motion interpolation. BFI causes motion artifacts (trailing ghost images) if the frame rate of the video is less than the refresh rate. Motion interpolation also adds its own artifacts.

>mpv's video retiming works some of the time, but means it changes the pitch of audio

The best way to use it is to set custom monitor timings (e.g. with xrandr) so that the adjustment needed is too small to detect. There are various scripts to automate this, although I haven't personally tried any (I just change mode manually).

>if your monitor has variable refresh rate why are you using retiming?

I have a VRR monitor, but I still use retiming because it only has a 6 bit panel, and VRR makes temporal dithering artifacts ("frame rate control") visible.