When you’re tailing logs on a server there’s still a “logging system“ (your ssh connection, tail -f, a disk with finite space) that can still “fail”. Probably in either case you’d work to fix logging and you’d hope that the system is simple enough to fix.
What's complicated about a syslog server? I suppose some applications like to spew out multiline logs (which are something you just can't process outside the source while maintaining sanity) but seriously, when you actually consider these things while writing the application, you don't need all that much to have something workable.
I was going to make a note that an rsyslog collector would be my only exception to this because of how simple it is but you still have to be careful because by default rsyslog is okay with losing logs in-flight.
But I would be lying if the typical logging setup was this simple. It’s basically all remixes of ELK and while they’re fantastic when they work there are a lot many moving parts that can individually fail.