My problems with bluetooth pairing tends to be with bluetooth speakers and cars. Cranking up the car and all of a sudden being on the phone with whoever my wife (in the house) is on a call with is pretty weird.
Also my car prioritizes connecting to my phone even though my wife is usually the "DJ" on a drive. And disconnecting my phone after we've already started driving means my wife has to get my phone out of my pocket/lap and turn off Bluetooth since the car offers no simple way to do so other than outright unpairing my phone.
That rough, our cars (both 2010s Toyotas) give a way to switch between phones, but it's about 4 button presses and 20 seconds to do that. It seems a car should be be capable enough to have multiple phones connected, and they would all just appear as sources you could switch between. Some probably do, but obviously no 2010s Toyotas.