The TVA is only a small part of time beauracracy called the Major Time Management Authority,whose total job is dealing with variants, monitoring astronomical things so that they don't veer of course, mind control for events like Thanos getting defeated in endgame, paper work, etc.
The time variance authority deals with Lokis, ONLY LOKIS, because goddexes of chaos can't help veer of course.
This has me conclude that either mobius is bad at his work or was TRYING to make loki go off. I say trying because there is no way lokis tears from episode one and his hopelessness was something more than an act.
