Sorry that you haven't had a great experience with our appeal system, personally I will at least try to check for appeals assigned to me a few times a day. However, for most staff, Olympus is not the top priority in their lives and schedules can fluctuate, so response time will always be different.
Appeals for shorter bans can be tricky to resolve during the ban sometimes (dependent on when the appeal is submitted, time zones, and as I said earlier with schedules of both the staff member and player). However, that being said, it is still worth it in my opinion to appeal, even if it just means that your next ban won't be longer than it can be. On another note, the appeal system is certainly geared more towards longer bans. Also, staff members are easier to communicate with over the ticket system for the most part, since we don't need to be at our computer to respond to support tickets.
As for your appeal specifically, your last response was 3 hours ago and that was after you replied 6 hours after his response, so that's not really a ridiculous wait time in my opinion. And as I stated earlier, staff aren't always available on TS on demand.
Unless it's blatantly not a rule break, higher ranking staff members aren't going to step on other staff member's toes. Most of the time appeals depend on what the staff member deems appropriate (i.e. being lifted (usually when someone comps/offers comp right after the situation or provides a new video perspective provided), reduced (this is usually for slight misunderstandings, unintentional actions, staff member being lenient, etc), or no action taken (usually blatantly intentional/severe or a very poor attitude/complete lack of accepting responsibility in an appeal)). As for same level staff (mod-mod or admin-admin) lifting each other's bans, while technically it can happen it's more complicated and once again is only done if the ban was blatantly wrong.