"Give yourself space to not work so you don't get burnt out" is only applicable if you have the expendable resources to do so, and the reason that many people don't is that our culture and society are broken for them. For someone like that, listening to people talk about things like "work-life balance" is enraging, frustrating, and demoralizing.

That said, if we're going to fix this situation, we're going to have to work together on it; which, for people who have the capacity to spend extra time on social issues, means putting their oxygen mask on first, so they're more effective at whatever it is that they're focused on. In many cases, this is precisely the kind of change necessary to fix the system.

My point here is that it's a complex situation, and it's correct both that a) there are bigger problems than burnout in the world and we should be aware of this and b) burnout is a real issue for some people, and that deserves support and attention too.

There's no reason we can't focus on more than one thing.