I thought you could if you have an account and accept the terms (including claiming to have a television licence, which I think requires a (British) national insurance number to obtain)?

Or do you mean as an American in the US?

Perhaps it's changed, but last time I looked the BBC had simple GeoIP blocking for anyone not inside the UK.

Not simple - they have an extensive blacklist of VPN servers too.

this provides an incentive for someone to provide vpn/tunneling service with IP pool large enough to prevent blacklisting to be effective

That doesn't last long.

The BBC use the same provider as a number of Vegas gambling services, and they're very effective because Vegas is willing to spend lots of money on forensic work.

You cannot do this even as a Brit in the US. Everything on the iPlayer (except radio) is geo-restricted to the UK, and they're really very good at playing whack-a-mole with the VPN services as well.