Keeping the log file tidy isn't just an OCD thing. If you're searching for a needle in a haystack, where needle is "suspicious login", and the haystack is "all of the login attempts from the past the months", your job is made much easier when the haystack is much smaller.

That said, the fail2ban defaults are way too low and I've locked myself out with them. They can be turned way up (ban after way many more attempts) so that there's no risk of locking out legitimate users. (Assuming your users didn't forget their exact password and then generated a small dictionary to try with.) On a server with potential misconfiguration, accepting passwords is one of them.