"Seriously compromise the security and stability of the phone" ? Are you serious ? Directing audio to headset profile is just like having an active phone call. If a call comes in during this, it would need to be treated like call waiting. If a call needs to be initiated, the audio would need to be stopped before the call can be placed.
Greanted that there is some additional work in dealing with this call flow, but I am sure apple engineers are smart enough to figure out a way to do it right.
I really feel the reason is more to do with marketing and generating additional revenue. It is not really a technical limitation at all.