Because international air law was set up to allow international transit, not to enable people to choose the cheapest, lowest common denominator option, and keep out of their regulators’ sight by flagging light aeroplanes out. The FAA are very clear that they don’t have, never will have, and don’t want to have, the resources to monitor N-reg light aircraft overseas.
Perhaps EASA should make it a bit easier to operate light aircraft in Europe then?
On a slightly different topic, would anyone like to take a guess at how much of a market is there for FAA flight training in Europe - both initial, and recurrent (flight review, IPC) ?