Payment in coinjoins is even simpler than that: you just schedule as many payments as you want and they will be done in one or more coinjoins. So, instead of registering scripts that belong to you, you register scripts that belong to the payees. Nothing is more private than that, at least in Bitcoin.
Also, there is a market for coordinators but you cannot compete for fee but for liquidity, time, minimum output size, leftovers, etc. We just fixed one variable, all the rest are still there. And the most important part: you don't need to trust on how trustworthy the coordinators are, they can't take you money and run.
