It would be nice, no doubt, to have errors in a convenient place. However, it's not feasible to expect this from osTicket if the PHP script bails with a fatal error, which was probably happening when you had the handler enabled.
There are already much better log viewers available, like Webmin, CPanel, or rsyslog. For example, you can configure rsyslog to parse errors and send to email or a log server.
Trivia: I've seen a personal osTicket server that a guy setup in his home as a log collector using rsyslog. It automatically creates tickets for errors he needs to fix in his lan.