The point of net neutrality is that without it, your new service will never have a chance to make any inroads at all, so customers won't know they can't access it. A competitive non-neutral market won't fix that.
You're assuming a world in which ISPs have managed to make themselves the gatekeepers for sites, which assumes they have the power to do so. Given competition among ISPs, no one ISP would have the power to do so, and a group of them getting together to do so would quickly find itself facing antitrust charges.
The ISPs don't have to be the first movers; enough megacorps paying enough ISPs to make a "free tier" would have the same effect, which is exactly what we seem to be discussing w.r.t. India.
This is already visible in the US with smaller sites; many video streaming sites, and subsections of even more video streaming sites, are exclusively available to customers of specific cable/sat network ISPs.