That would be stupid, you would have maybe 4 people who could even get a full lap at on OK throttle, maaaaybe with enough laps JK or cod piece could put a real time down but that's doubtful. So every week would just be "watch stars spin out in an expensive car most people can't afford" Base model may only be like $35,000USD/?25,000 GBP which is cheap for what it does (remember the one on top gear wasn't the base) but that's still over 2x the current car. Same with the Caterham cheap for what they can do but far from cheap or reasonably priced.
That also makes the available "stars" much smaller, do you really think you're going to get somebody like Kristen Scott Thomas or Fiona Bruce to drive something like that?
The "fastest" car I would like to see would be Abarth 500, anything other than that and you might as well change the name.