It doesn't seem out of realm of possibility that KYC/AML/whatever will be enhanced for cryptocurrency to/from fiat exchanges, and I don't think cross border nature will exempt to (i.e. exchanging fiat to crypto on a foreign exchange) - look at non-EU companies charging VAT for EU customers for example.
Take Monero for example, the potential privacy coin, some people think that it will be next Coinbase currrency (I think this is a pump though as they grasp onto any hints like it's solid) and that they will fully satisfy regulator requirement by Monero Coinbase users withdrawing to their own Monero wallet and providing Coinbase the viewing key so Coinbase can say to regulator it went from JohnB to JohnB. I have a hard time believing this will last long and I doubt Coinbase do to, regulations are a moving target and loopholes will get closed fast or at least eventually.
Drop fiat at the edge though and then it's a different game, but what do people start from? mining? mechnical turk tasks? some global airdrop for every human on the planet - is this was even remotely possible that would be interesting.