Ok.. this is strictly my opinion as to if it were me in this situation: NO WAY!

A good therapeutic relationship with a T includes transference. I don't trust any psychiatrist enough to allow them to try any kind of therapy anymore, only psychotropic medication management. I would doubly question the arrogance of the psychiatrist for wanting that. Many T's do dbt along with ongoing therapy... DBT is not a cureall for land's sake.

Going cold turkey from ANY supportive relationship is "dangerous" for me... and deadly if it were from my pscychologist.

Trust your instincts. Psychiatrists can be wrong. Hopefully you can say no and still have their support for medication. Be sure to discuss this at length with your T... I know in the realm of clinical psychologists, to "take" a patient away from another psychologist harbors on unethical practice. IDK about this situation, but it smells the same to me. Remember IMO!