What would motivate the carrier to foot the bill for access to a single domain if not some kind of sweetheart deal?

I think this bodes very badly for the internet. We need to maintain a model where:

1) I pay for access 2) I access whatever sites I want

If anyone but me pays for my access, they're going to want to make back room deals, make favored sites faster, make sites they don't like inaccessible, and generally destroy the level playing field of the internet.

This is a first step. "Let's search for that on DuckDuckGo." "No, that costs money. Google is free." Boom, innovation stamped out.