Even if you really wanted to have it be trunk-only, I don't know why you wouldn't make everyone push to a feature branch, then have automation for running tests and merging after they pass. Plus, where's the code review in this process? Even if your team is all amazing developers somehow, it's insecure to have a standard process where developers are pushing unreviewed code directly to production.
Fundamentally this all seems like a misreading of trunk-based development, though. The whole idea was to get away from old Subversion-style branching, where there would be long-lived branches running for sometimes several month. If you were a company that moved from svn -> git, trunk-based development was a way of communicating that branches were cheap and disposable, and merging was quick and easy.
I'm questioning the logic of having a workflow with a not-uncommon case of "this is on fire now everyone stop what they're doing and help me fix it" which is exactly what you'd have here.
Not saying I have a better solution off the top of my head, but "just fix it with another commit" is a big red flag IME.