Two stroke question

So, I have never received a detailed answer to this question....here goes. If two stroke motors make such incredible power out of a small displacement (remember the gp500's...180hp?) how come a series like NHRA never built or started a class for two stroke? I wonder what the theoretical hp would be from say a 350 cubic inch two stroke? The powerband/traction control could be handled electronically, they would also sound amazing. I know it wouldn't be relevant with today's auto buyers and of course, pollution would be hard to tame but it would be exciting. I remember a couple years back seeing a guy put an outboard in a car....can't remember the results though. I think Saab did some two stroke stuff long ago....anyways, am looking forward to an answer. Cheers.

 

Hmmm....I had several race karts, three 500cc 2 stroke super bikes and a couple of sleds and never witnessed them leak....even when running rich. I guess there would be a bigger potential for that with a much bigger motor though? I would love to see how much power a small block 350 two stroke converted chev would make!