Given that the only way for those websites to block VPN traffic is to block the IP addresses of all known VPN exit points, what you would see is first the VPN providers regularly rotating those IP addresses, and second people simply setting up their own VPN servers software in rented VPS in cloud providers anywhere in the World.

You don’t need a full blown remote session, just a VPN server with an IP address which isn’t yet blocked by such a site.

Now, the sites might try and block this by only allowing in connections from know ISP blocks of addresses (which would theoretically only be direct connections from individuals not using a VPN), but that’s way less reliable than merelly lists of IP addresses of the VPN servers of big providers, plus it would block thing such as the entirety of Amazon AWS.