People often push back because of the link being YouTube

Idea to mitigate this (or for any other domains people get screechy at):
First entry to be some redirect script, even perhaps a community-maintained one as from what I dug on the matter a while back, replacing the domain in a link with e.g. Violent Monkey is pretty trivial, at worse requiring some regex and JavaScript knowledge.

The problem with a static list in a sidebar is exactly what you said: public instances come and go, and in six months half the links are dead and someone has to keep pruning them.

A lower-maintenance option might be to link to the things that track health instead of the instances themselves, e.g. the official Invidious instance list that shows uptime, plus a one-line mention of LibRedirect (browser extension that rewrites YouTube links to a working Invidious/Piped instance and rotates when one is down) and FreeTube for desktop, which doesn't depend on any public instance at all. That way the sidebar stays correct even when instances disappear, and people sharing videos here can keep posting the plain YouTube link without it being a problem.