To your point--no psychiatrist will institutionalize someone on your testimony, but a judge might. Depending on the state, a judge can send a person on a 72-hour court order to a psychiatric facility on the basis of an affidavit from a concerned party. If you can convince the judge, which in my state is apparently not difficult, the person wins a psychiatric admission.
"Lock em up!" feels like a great idea. Until you wonder what happens between them hearing about it, and showing up in court. Or after they are released from the psychiatric admission.
This is a plan that can backfire..badly.