How to change job output log location, when using Ola Hallengren's scripts
I’m going to reword your questions a little:

Q: Should I log Agent jobs directly to a remote file server? No, because if you lose network connectivity or the file share goes down, your Agent job could fail. Your Agent job might not require network connectivity, like an update stats job, so that failure would suck.

Q: If I want to centralize Agent job history, how should I do it? Consider logging to a table (and Ola’s scripts support this too.) That way you can centralize the data in whatever method you like, like replication or log shipping. I like logging to a DBA utility database, and then restoring that from all my servers to one central server daily. Then I use union all views to combine the data from all my servers. It’s not up to the second, though.