Oh dear God! If it's a surface cavity, sure you can go without anything to knock out the pain, but anything too far into the dentin and it'll hurt like he'll because of the nerves.
That said. Gas knocks you out. There are two problems with that. 1) some people don't come out of it, and end up going into cardiac failure. 2) it takes longer to recover after the procedure. That's, they either have to try to move you to a recovery room or lose the room for the period of time you need to come out of it and get on your feet.
Neither problem exists with the shot since it's local.







