And it's not a problem if the service provider trusts only one mint. We just need one mint that is trusted by both parties, and the negotiation to find a trusted mint could be done automatically
How is that any better than cashu, from a risk-of-rug point of view?
The cashu folks are working on a proof of liabilities scheme to work alongside the obvious proof of reserves that mints could run (link below) . I haven't studied that yet, but I should and it might solve those problems
https://gist.github.com/callebtc/ed5228d1d8cbaade0104db5d1cf63939
Discussion
The probability of a common mint approaches zero with more users and more service providers.
With each service wanting self-custody, the user would have to approve every mint for every service one by one.