You also do not repeat every single thing, but pick what you think is essential. The other person will then immediately see if something is missing from the summary, which overall leads to weeding out what is important from the not important, and eventually escape thinking loops. Without you adding anything, just by selective removal, you end up with the essence of the problem. It’s a process of distillation.
Known techniques for example are nonviolent communications and Focusing. That is a multi year accreditation process.
So like a therapist?
I'm not sure what experience you have with changing people's beliefs, but so far this isn't the way to do it.
It sounds like your argument is "If reflective listening is better, then it should be used universally." I'm not making that claim. The claim I'm making is that reflective listening is good for emotional validation.