I am in Boston and I find that most, or at least many, therapists do take private insurance. It's more common to see Ts not accept public insurance (or the public plans don't cover them). In terms of private insurance, I tend to see more psychiatrists who don't take insurance, but in those cases they are usually older, Ivy League professors with very few patients.

Ts who practice in affluent suburbs can probably afford to be cash only, although the ones I see are in those areas but still take insurance. Actually, my plan is an HMO and I have unlimited coverage for psychiatry and therapy. I think Ts who refuse insurance by choice probably don't see therapy as health care but rather a luxury, almost like massage therapy.