That's basically how many old human-labor matchmaking services work, insofar as the matchmaker gets a lump-sum payment at the beginning, and then spends an unbounded amount of labor doing the matchmaking until it works out. The matchmaker is incentivized to make a good match as efficiently as possible, as their profit-margin decreases linearly with the amount of time they spend on each "case."

That just sounds like the optimal solution is to do zero match-making labor.

If it was a one-time game, sure. If your game relies on future business, word-of-mouth advertising, and not being arrested for fraud, it’s a bad choice.

Eh maybe from an efficiency perspective on profit vs labor, of I can get one person to pay me $100 to matchmake for them, then do nothing, I've got an infinite return on my effort, but if I want to make a living doing this I need to have some success stories to keep the $100s coming, so some effort is needed.

I like the alignment of incentives here, but "match" would have to be defined better. If it's a literal match (mutual like) it would effectively be a per-pay-like and wouldn't work. Maybe something along the lines of "matched, chatted, met, stopped using the app for X period of time"?

Yep, I've thought something like that:

For every month that you use the app to a certain degree (number of viewed profiles, page loads or whatnot) I will give you back 1/nth (1/12th) of your deposit. If you don't use it enough, then I'll "keep" that month's budget as a subscription payment. The idea is that once you match with someone, you will stop using the app, and the rest of the money will slowly go to me.

I am convinced it could be a good model, of course as with everything, there are several things to be solved before making it a sound business.

I know your idea is very theoretical but what happens when I exhaust the deposit? Do I stay around and earn money or do you kick me out?

And if someone finds a match but doesn't inform the site you lose out, no? I expect a lot of people to be dishonest if it means getting a bunch of money back.

Cheapskate users will keep dating (or even just looking) even after finding a good match.