I'm looking for examples of companies acting as marketplaces in the sharing economy where users could cheat after the initial transaction, but the company has figured out how to effectively stop it. As an example of the problem: mopp.com. Once you've used the site once and have a cleaner, there's no reason not to pay the cleaner cash directly - it's easier and cuts out the middleman. Other examples include dogvacay and similar. As an example of what I'm *not* talking about - Uber. It's a dual-sided marketplace company within the sharing space, but no one's going to go around it, because it's a one-time transaction. Likewise AirBnb (for the most part, plus they also sort out the international transactions for you).
Here are a couple of marketplaces where the user will always have the option to "shop" outside the system but always comes back because of convinience.
Udemy.com, Tareasplus.com, Clarity.fm, flippa.com, 99designs.com, fiverr.com,
As you mentioned, most marketplaces that have reoccurring transactions between the same parties seem likely candidates to move to direct transactions.
Common reasons why direct transactions don't happen:
1. Trust - Generally the marketplace has built a reputation(ex: Ebay) and will provide some confidence that the transaction will happened as planned. Sometimes formal insurance or guarantees are in place.
2. Convenience - Transactions often involve tax and do the parties really want to be responsible for calculation and remittance of this? It used to be that payments were a barrier(ex: how to get paid by credit card) but there are enough fintech payment solutions that this is not as large of an issue anymore.
3. The Network - Often there are other value added services of the marketplace that compound the more you use it. Whether this is suggestion algorithms or activity history that others can view. Think about a scenario where the other party needs to be replaced on short notice... would it have been easier if you were still engaged with the network?
These are some common ones but if you have a specific situation in mind where the friction to leaving the marketplace is low, I am happy to discuss potential solutions to keeping transactions on marketplace.