The problem is that your solution is not feasible. F1 is the fastest motorsport series and that is how the public views it.
Is it? F1 isn't the fastest series in reality (IndyCar goes faster on ovals, and in a straightline drag racers are faster still). And I haven't seen any actual evidence that the public sees F1 that way.
If you strip all the downforce aero bits from the car like flip-ups, wings, diffusers (!) and the like you will end up with cars that will be totally uncontrollable and probably slower than a V8 Supercar around a track.
Really, why will the cars be totally uncontrollable? Go-Karts don't generate downforce, and they're not uncontrollable, and nor is a Formula Ford without wings. Also, why would they be slower than a touring car? Downforce doesn't really help much in slow corners (you generate more downforce with speed), and I'm not sure how a 620kg car with stickier slicks and 760hp is going to be slower than a 1350kg cars with narrower, less grippy tires, 620hp and maybe 700kg of downforce.
No amount of tyre technology or bigger tyres will make up for the tremendous amount of grip lost through the removal of aerodynamically-generated downforce.
How much grip will actually be lost though? It's pretty hard to quantify, in particular as depending on the track, the difference would be either more or less significant.