Unless the difference in car sales tax vs normal sales sales tax in your state (if that ends up being how it works) exceeds the 2% cashback you’d get on the credit card. I guess if you opened a new card with a substantial sign-up bonus, the percentage might be much higher.
Do you find that it's more difficult to momentarily turn on your high beams or wipe the windshield after getting sprayed by another car than it is in a vehicle with controls split to both sides?
I'm 23 so I haven't driven very many cars over my lifetime, but all the ones I have driven have the light controls on the left stalk and the wiper controls on the right stalk. The muscle memory of "pull right stalk towards me for wiper fluid" or "push right stalk up to trigger the wipers once"...