Here is the problem with the idea. You have this every Friday night at Commerce. The street cars running regular radials don't lay down any rubber on the track, so you basically will waste the track prep. If you don't think so, go to Commerce and see how you will run 0.5-1.0 sec slower than MMP, Steele, SDR, etc.
The V8s will still have the advantage. The serious guys will just run a bigger width and diameter street tire, and will still have a good patch, since most will be RWD. The FWD imports will mostly be stuck on 7-8" width wheels max.
Additionally, most of the imports and street ready cars will likely be manual. Automatics will have the advantage as almost all street tires will be radials. The stick cars will shock the tires harder, so the fast autos will have a huge advantage there also.
Slightly built, FWD, stick shift cars should suffer the most - which is what most of the people on this forum would be.