It does a lot of what you suggest. I've started from a position of "so you know you want a psychologist" because otherwise the scope is just overwhelming.
Like people have found, fit is the most difficult thing. I think we can improve this with data. But until someone's figured it out, I recommend always calling a therapist on the phone and talking to them a bit, before committing to a session. The phone is scary, but a bad intro call is much less draining and expensive than a bad session.
We're working on enabling online appointment scheduling for the reasons you say, but getting a uniform booking interface for thousands of individual psychologists turns out to be a huge task.
If people wanted to have a look around we have a test link  so the human clinical staff know that you don't need help.