After reading @Knuckolls post a couple weeks ago about how he got his old accounts unbanned, I decided to give it a try myself.
I appealed for bans on two of my older mains, one for RS3 and one for OSRS. After about 2 weeks I got an e-mail today saying both were unbanned! Luckily my OSRS unban says it was "applied in error", and the RS3 one was "an extremely rare case where people change over time" (jokes on them).
Hopefully this motivates other people to do the same thing and maybe get an account unbanned
For those asking, this is the link. You don't have to write an 12 page essay describing in detail how "your best friend hacked your account and botted on it", you literally enter the e-mail and display name and they review your account.