Answering my own question, but now there is:
Which does exactly that: "generous" members bid to go on dates with "attractive" members. It's done in a little too gender-rigid fashion, in my opinion, and also seems very openly to be skirting prostitution laws, rather than outright avoiding the potential linkage altogether.
Still, interested in any other competition, or failed prior attempts…
What are the arguments against paying singles to participate in online dating sites?