It’s the same as their influence on the internet; limited and not really effective unless you’re interested in doing everything by the book. China puts a lot of effort into maintaining the Great Firewall, but because of the decentralized nature of the internet, there will always be a way through the restrictions.

I suspect the same will be true of crypto – if you want to be entirely above-board and legit (and want to acquire fiat money), you’ll need to go through a centralized layer with KYC and regulation and consumer protection.

But, like the internet, the decentralized nature of cryptocurrencies means you’ll always have the option to circumvent these controls. If you want to acquire fiat, any such circumvention may be legally precarious, but if you don’t depend on the centralized layer then there’s nothing anyone can do to stop you from transacting with a consenting counterparty.

Basically: let them regulate the space. It will be good for consumer confidence, since 99% of people willingly accept regulation in exchange for protection from FDIC, CFPB, etc.

The centralized layer will benefit those people by mitigating the risk of total wallet compromise (your bank can reverse erroneous charges, and many say that any crypto “bank” needs the same ability to compete). If you want to opt-out of that, you can do so, but at your own risk (financial and potentially legal).