It would be great and in fact a very important thing to make it possible to bind a control profile to a specific aircraft. So that when the plane is loaded, a specific control profile is selected. This will save you from manually switching the profile every time you change the plane (and the chance that the user will forget to do it himself).
Agree, it is impossible to use a single profile for different types of aircraft.
P.S. It is also worth considering that it is better to contain only changed assignments in a custom profile, and not everything in a row. If the command is not changed, then take assignments from the default profile.