“amateurs setting up this nice person with that nice person who both seem to and say that they want the same thing, and seem to be a good match in theory.”
many shidduchim have been made exactly the way you described, LB
When I dated, I always preferred the suggestions that came from people who knew me than from a professional shadchan, who often had some preconceived notion of whom I should marry without knowing me or even meeting me.
No matter where the suggestion comes from, it should be checked out personally.
If the shadchan feels that they are not competent to do more than suggest a name, and they can’t handle the follow-thru/advice that is needed, then a third party can be enlisted -say a dating couch or other mentor who can be the one to talk to each side, and help the relationship progress as necessary.
But I would not personally set up some anonymous person online knowing nothing about him.