The problem is that most of that work is not something anyone can pick up.
Regardless of the coding, one would first need to be familiar with git or VCS in general.
Also, you would want people to go back to normal jobs when they can. This would lead to short stints for all employees which I've always found to be one of the best predictors of bad outcomes
Obviously it wouldn't work for everyone but for those who have an interest in computers it would be a nice option.
I was unemployed for a while in 2008 and I'd have loved it if I could have got paid minimum wage for working on open source rather than just getting jobseekers allowance and searching for jobs that didn't exist.
Plus I'd have learned some valuable skills that would help me find work anyway. And it would have increased the numbers of IT savvy workers. Seems like a win-win-win.
Edit: I mean from a society perspective you pay a tiny bit more for a real gain, without reducing labour from the private sector.