There are other online services like Uber and AirBnB in which it is much easier to cheat by communicating with your counterpart outside of the app, that way you don't have to pay commissions and so on. It's a serious problem for them.

But this hypothetical online service marries people. Fraud is much riskier there, because divorce can be extremely expensive if your partner-in-fraud doesn't cooperate.

> the free market still needs a central authority for any proofs

Isn't marriage a relatively centralized institution? The central authority that marries people can easily provide proof that they indeed married some people.