I think the key here is that AML/KYC is mostly for businesses while transactions between individuals are usually not affected (except for special items like firearms). So in Switzerland for example there is a 25 000 CHF limit for businesses for anonymous cash transactions. However individuals are not affected, so that a p2p 100 000 CHF cash transaction in Switzerland would be perfectly legal.
in Southern Europe the limits are very tight but discount airfares could solve that problem.
The REAL problem with p2p transactions is the scammers. There is a market opportunity for secured p2p meeting places IMHO (counterfeit checking, escrow et cetera).
AML/KYC laws still apply when people are dealing on a p2p basis, however law enforcement is generally not going to go after you for not following these regulations as most people who participate in p2p transactions are too "small of fish"