From a US perspective I've been following this thread with a mixture of amazement and amusement. It's certainly a miracle that pilots aren't dying by the thousand without the wisdom of the EASA/CAA.
In FAA land, once you have a PPL-ASEL you're good to go in any single-engine piston or turbo-prop airplane less than 12500 lbs. (Well, endorsements are needed for certain characteristics, like retractable and high power, but they are not type specific).
Any further regulation comes from insurers and (for rentals) the aircraft owners. Any FBO or club will want an instructor checkout before they'll let you take one of their planes out on your own, even if you claim to have 5000 hours in type. Though if you really do, it won't take long. I could go out and buy myself say a PC12, and the insurance would want a number of things including most likely an approved training course. But the FAA would be fine with me just jumping in and trying to fly it.