I don’t think there’s really a good model. If the app charges when a match is made, the consumer is paying without really knowing of the match is good. As I understand, this is the model early dating sites used. If the app charges for access at all, then it’s incentivized to keep you from finding a match, and the overall pool of people shrinks from the barrier to entry. Charging once you’re satisfied with a match isn’t practical without some kind of binding contract, which I imagine most people will not want to sign.
It’s almost as if you can’t commoditize emergent social behavior.
I've sometimes wondered if dating apps are best served through some kind of nonprofit decentralized format, maybe something grassroots, or through the government or something, precisely because of the issues you raise. I admit that might sound a little loony but dating or pairing is a fundamental human activity, and it doesn't seem too farfetched to me to think that people might build out something outside of a profit model. Also, some countries are starting to openly discuss declining birth rates, with government actively encouraging mating, so I could see something like that being developed in certain settings.
I also have a hunch, though, that some of what makes relationships click is hard to formalize in an app focused on dating per se. In person chemistry, development of an initial relationship without an explicit shared dating goal, and so forth. Sometimes I wonder if it would be better to just incorporate dating options and features into a more general purpose social app.
It’s almost as if you can’t commoditize emergent social behavior.