You generally don't get technical interview performance feedback because technical interviews are constrained by the interviewer to put themselves in a technically confident light against the candidate. The interview is as much a crapshoot for the interviewer, because they might be less/more/similarly skilled to the candidate, but they absolutely cannot reveal themselves to be less skilled because they would undermin…
My favorite interview question is a real life issue I faced where a short sighted database design wound biting us in a pretty serious way. It's a good technical problem to talk through, and provides a lot of useful information about the candidate, but it's also an excuse to set very clear expectations that I'm not looking for the "right" answer (in real life it took half a dozen smart people a couple hours to come up…
You're also right that sharing the problem does place you in a position of vulnerability. It's perfectly possible that a candidate will think 'what a bunch of idiots to have gotten themselves in that mess in the first place'. Or worse, when they realise how you solved the problem, 'wow, they think they solved their problems? They're in an even worse spot now'. So I appreciate that you see this as being humble and exposing the candidate to an opportunity to know more than you.
But the reality is, when you solved that problem, you:
1) knew all of the context and constraints, spoken and unspoken
2) had a team of folks around you to bounce ideas off and collaborate on the solution
3) had access to google, stackoverflow, etc.
4) did not have to come up with a solution inside a small interview room, within a few minutes, while being judged by someone who has decision rights over your future employment
5) crucially, had found yourself in a position where you needed to know how to solve this problem. If you hadn't had that need, you would never have acquired that knowledge. So unless the candidate had also faced this exact problem, why would they know how to solve it? You work here, and you didn't...
And while it might be nice to hire someone who can, under interview conditions, jump right to the right solution shortcutting all of those processes - it would obviously fill in a knowledge gap your team demonstrably had - looking for a candidate who has already learned something that came as a hard-won lesson for your team is like a general building up an army to better fight the last war.
You can do better: Use the problem as an example of the sort of thing your team has struggled with, and ask the candidate to give examples of similar problems they have solved in their own career. You are hiring them for their hard-won lessons, and adding them to your own, not looking for someone who happens to have also won the same lessons you already have.