My older FlySky Rx's will work great. The newer ones it will remember the bind from flight to flight, just as long as I don't switch models.
When I switch models I have to rebind the newer Rx's, the ones using AFHDS2A.
My work around, I made a remote bind plug using a servo extender on the bind plug.
Fwiw, I haven’t had this issue with my TX16S. I have a few different models of AFHDS2A receivers. I believe my binding procedure is to turn on the transmitter, put it in bond mode, put the bind plug on the receiver, plug that in, confirm binding, disconnect bind plug, then unplug the receiver and plug back in to confirm. I’m on the latest version of EdgeTX. Not sure if this helps.