Do you think this would be a good idea?

May be...

Not really.

Do you think that F1 would be better in an elimination format?
So theres 22 cars atm right? Each race could be 44 laps, every 2nd lap the driver coming last is eliminated, what do you think of this?

Not for Formula 1 as is.

If they ever had something like NASCAR's All-Star race it would be a very cool idea.