How do you plan on reinforcing that hole? 6' down needs some real engineering to prevent collapse. It might cost as much as a lift. You'd also have to consider safety when not in use. You would not want animals or children to fall into the hole. So it needs a cover that a child cannot remove.
Then there is the whole don't drive your car into the hole (I have heard stories about the, lol).
So I'm gonna vote no on your pit idea. Is your driveway concrete? Jack stands can help.
BTW, don't use blocks/bricks with voids as vehicle supports. They have been known to break at inopportune times.
Bad:
