My prefered method has always been the chase cam, or 3rd person as you call it.
When I play a racing game, I like to view the car and it's obviously much better to look around for other cars on track as well. I tried the bumper view and it's atrocious for me, can't hit any breaking points and it's way too low.
I can handle the hood camera fine though but I still think the chase cam makes me handle corners better.
Cockpit view is amazing, but it obstructs you a lot. It's impossible to be implemented in the same way as real life because in the game you have no peripheral vision. Unless it's VR, and even then it's still not the same as IRL.
However, if it's a car with a center cockpit, like most LMP cars, Formula cars or the McLaren F1, it's much easier to handle. Even better if it's an open cockpit.
I've gotten so used to this chase cam since the GT4 days that it no longer bothers me. However, I do agree it could be more dynamic than what it is.
Forza does a good job at this, but Assetto Corsa is horrible, way too dynamic, it's one of the main reasons (outside of the game having horrid controller optimization) that I don't play Assetto Corsa.