Hmm..
Having read the above I simply want to weigh in a bit of a counterweight.
I am a TRI/TRE for a legacy European carrier, and I can not recognise this type of environment at all. At my outfit, I know of no trainer at present, who bullies colleagues during LIFUS/sim and should such an individual repeatedly "show up" in the rumour mill, action would be taken promptly by our Training Management.
As been mentioned, having a TRI/TRE you represent your national aviation authority first, and your company second. Personal integrity / suitable personality / a true desire to teach and improve safety standards are the cornerstones of a Training Captain, period.
As for the CAA to conduct all checks etc, that is simply hiding the real problem, which is a toxic company culture and a bunch of no-principle individuals running the training dept. Sad story..
my 2 cents,