A quick look around the web suggests you can do high performance driving events on serious race tracks with no experience at all. You may be required to do some laps with an instructor in the car and they have tight restrictions on passing. They'll probably want to check that your car isn't falling apart for obvious reasons.

If you want to do wheel to wheel racing with other drivers, then there's a license requirement involving a couple days of training with a four digit price tag.

Maybe we have different thresholds for what counts as "bureaucratic shit", but there seem to be some good options to drive fast under controlled conditions and compare your results to others. The most exciting and dangerous versions of it have some gatekeeping and I imagine most of the participants prefer it that way.