I think this should be considered as a way to prevent previously fixed problems from reappearing again. I don’t know how SE does it, but apparently not well enough, that we get to see some old bugs reemerge from time to time.
Seems like a no-brainer to me.
Well, at least in an idealistic sense. A goal to strive for, but in reality there’s always occasions where it doesn’t work as well as in the happy examples.
But in general, yeah, we should be using automated testing. With so many free CI services available to public projects, it would just be a wasted opportunity to not do so.