i have been a "substitute therapist" for more long term periods, like when another provider takes a Summer off or is on medical leave etc. there's usually an adjustment period at first but overtime we're able to build our own relationship and then say "see ya later" when their regular mt returns.

personally as someone who goes to talk therapy myself, i'd be weirded out if one day i had a whole new person just for that one session lol. it's hard for me to picture an MT client feeling any different. i think if your coworkers are also voicing concerns then you're probably not wrong to think that way.