Not all therapists take insurance. One of the two I see does not. She will provide info if the client wants to send it in and see if they can get reimbursed, but she does not get paid by them. She also bills for phone calls over a certain length (20 minutes or so I think - I have rarely called and never wanted to talk to her more than a minute or two).
None of the ones I saw in the past did either. I don't use my medical insurance for most things. I prefer to (and have the luxury of) paying out of pocket for most expenses.

There is a huge problem in letting insurance companies dictate what a client can and cannot get in terms of help. IT is one of the reasons I don't think the medical model for therapy is a good idea.