>Did you ever had the "pleasure" of a server grinding to a halt because the logs filled up all the space?

I've never seen this issue on any systems I manage, mostly because they all have log rotation.

>but I find people not looking at logs a rather weak argument for letting them get spammed full with garbage. Certainly terrible hygiene, at least.

Why is it weak argument? If it's something that doesn't materially impact you, why should you expend effort into remediating it? Hygiene is only important for things we interact with on a regular basis. We as a society don't care about the hygiene of the sewer system, for instance.