If you make a turn using only keyboard, the view goes down to the pilots legs.
You can make the same turn using mouse, and the view does not go down to the pilots legs.
When I turn, I always use both, turns faster and you can see where you are going.
If you really want to see everthying (and you want that) use C+mouse to look around while turning, even behind.
Bind free view to middle mouse button, or whatever is easiest to press.
Can be kind of goofy, but you should now be able to sharp maneuver and free look if it looks like this: