I do drop and fills on both the coolant and the M/T with a flush on the brakes. My local “mom and Pop” independant refuses to do drop and fills for coolant,if you want to be his customer you must allow him to use his coolant flush machine.
A proper auto trans flush (with filter replacement and a real gasket on the pan)is not dangerous to the transmission,just expensive.
I have seen some pretty bad results in doing auto trans flushes. You must open the trans. fluid cooling circuit and some times people break off fittings,break stuff getting to the point where they open the circuit or don’t securely re-connect everything.
For GM many times the place to open the circuit is at the radiator and the later model clips and connectors can give inexperienced people fits.