I've had one good experience with therapy, but it wasn't for my suicidality or depression, it was "occupational therapy" to help me integrate into a new job after having quit my previous job due to depression.
I think the reason it worked well was because 1) I was a willing participant -- I wanted to be able to function well at work, and 2) it was solutions-based, so we didn't do any delving into my past or whatever, we just identified a problem (ex. I don't feel like I have enough oversight/feedback from my superiors, so I don't know if what I'm doing is correct), and then brainstormed one or multiple solutions (ex. set up a weekly check-in meeting with my supervisor).
After a few months of this, I was successfully integrated to my new job and we thus stopped sessions.
All that to say, I think therapy can work when there is a clear, specific goal, shared by both participants, and a willingness on both sides to reach that goal -- hence why it would never work (at least for me) for my depression/suicidality. Because my only goal is an exit, and I don't wish for that to change.