There used to be such a beast. It was called Can-Am, and the rules were basically that cars had to have two seats, fenders, and at least one engine. Other than that, it was anything goes. It made for spectacular racing, but tended to be dominated by one team at a time, and it was ridiculously expensive. It was ultimately shut down for cost reasons.
Not the sort of thing you could bring back today, even without the cost concerns. The "let's do everything we can do to make this fast" cars competing in that series killed a lot of drivers.
Something like the Porsche 917k30 was capable of close to 1500hp. (I can't imagine you'd actually run on race day with that setup) My dad and his friends commented on watching that car many times, and specifically the amount of noise that it made.
That car was illustrative of a few of the problems with the "let's just allow the teams to build the fastest cars they possibly can!" notion. Teams didn't pay as much attention to safety in general as they should have in the seventies, but more to the point: the performance differential between some of those cars - racing on the same crowded track - was just too extreme. There is no safe way to run when that extreme difference exists.
We're talking about the most well funded teams in the world; no chance of a small upstart coming in with a low bankroll and making a splash anyway.