Hah you make a very good point. I don't want to change the look of the car's interior, so no I don't want to fit an aftermarket head unit. However, it may be that the newer version of my head unit does all this, so I could look into getting one of those.
I'm not 100% sure that it would take all the steps that you're talking about, though. The phone would be connected to the car by bluetooth and aux via bluetooth. If the phone rings, the head unit would switch to the phone setting on it, and then I think I could take the call, and at the end it would switch back. The head unit would have no idea that you're involving your phone twice.
I always used to have to shout at my phone anyway, though, so that's not a huge issue.