To be honest I would expect a strength trainer to be in the Arena, it kind of makes sense. Moving them is ok too, but there has to be some logic behind this - like who that NPC is, why he possesses those kind of abilities and why he teaches them.
Now don't get me wrong, I love going to the Bronze doors, but not to train strength. That's kind of wierd. I would suggest however that there are NPC's in various places in the game which duplicate some of the others' abilities. Motivating a player to visit some remote regions in the game by placing training NPC's there sucks. There are better ways...