But looking at overall force diagrams, I cannot see a big difference between a current corner, say, with downforce, and an oval corner without the donwforce. Adding or removing downforce might make the diagrams more complicated, but basically the weight and centrifugal forces ensure that tires have to deal with a diagonal force while cornering.

So what is really stopping them from racing in ovals or in grip limited very banked corners? (The bank in Indy is currently not grip limited). Engines? Too high speeds? Is there a subtle effect acting on the tires?