F1 would be unworkable in the Olympics.
Red Bull would compete for Austria, but whoops, they use a Japanese Engine.
McClaren would compete for England but whoops, they use a German Engine.
Mercedes would complete for Germany but whoops, they use two British drivers.
Ferrari would compete for Italy but whoops, they use a French and a Spanish Driver.
The only team with chassis, engine, and drivers from the same country are Alpine. And well they're standing 6th at the moment in constructors. They're ahead of the back markers but not up to the standards of the good teams.
I really don't think any of them would be willing to break up a season to build a special car for the olympics and scramble around to find a driver from their country.
Oh wait. I think I see the Nascar entry from Camaroon.
