This is my opinion.
You can't expect to have a successful boutique psychotherapy or psychopharm practice right out of residency/fellowship. For psychotherapy, you need to get further training through an institute, and that will take quite a few years. And, you have to pay your dues. Since your practice is dependent on referrals, you need to establish your reputation. You will have to earn a good reputation: for instance, you initially will have to say yes to pretty much all the referrals that come your way- and there will be 'doozies' in these referrals. You need to take these referrals, because, if you keep saying no to these internists, they will not even bother bringing up your name to their patients, since they will assume you would say no anyway. So, you do this for a while, as you fork over big $ to attend a psychoanalytic institute and get analysis yourself. Then, you will start to get referrals you actually want, and will fill up a practice slowly and eventually, probably in your forties, be able to have a full-time boutique practice. Notice I say full-time. It is hard to fill a full-time practice doing all psychotherapy, but if just want to do this a part-time, it probably won't take as long.
I know a number of therapists who do this, and they don't take insurance, and they don't take cluster Bs (anymore) and they do very well. And they are all my parents' age. Oh, and I do live in a major metropolitan area, where $ is no object by these patients.