I am not sure what to do about the burnout problem. The way he described it is very on point though. Since everyone working on the project is overloaded there is a great feeling of things only get done if you do them.
Most of my open source work was in the pre-GitHub days when we used mailing lists, not pull requests, to build community. I do think there was something better about that for the project itself as it encouraged a lot more discussion and community building. PR's and Issues become silos and are not great for general discussion. I think they also encourage drive-by contributions which honestly are intoxicating initially but once you see people are not coming back become defeating.
All volunteer organizations have to fight burnout. Any time you start feeling like things won’t get “done” unless you do them, you’re on that road.