I worked as an insurance coordinator and psychometrist for a clinical psychologist in private practice for about a year and a half, and I was quickly disillusioned by the idea of pursuing a career in private practice.
Our practice's standard non-insurance rate for psychological testing was $150/hour, but most insurance reimbursement rates were between $40-80/hour, so generally speaking we were taking a 50-75% hit on all insurance cases. I learned a ton in this position, but the most valuable thing I learned was that a successful private practice will have a lot of business in areas not covered by insurance. We worked a lot with psychoeducational and forensic testing, since these were areas not generally covered by insurance, since they're often deemed 'not medically necessary'. A standard psychoeducational evaluation would be billed for 8-12 'hours' of testing (including administration, scoring, and write-up), and since people usually had to pay out of pocket, this is where most of our bread and butter would come from. We also worked closely with several attorneys' offices (forensic/legal testing isn't usually covered by insurance - i.e. DUI/DWI, violence risk appraisal, sexual deviance, etc.) and with a number of state agencies (corrections, work release, juvenile justice, etc.) that were all paid for outside of insurance.
Insurance companies are a necessary evil because they increase the number of patients coming to your office, but in exchange they (often) gouge you on reimbursement. In addition to the significantly reduced reimbursement rates there are literally hours (non-billable) of insurance verification, authorization, and claims that you have to do for every patient - sometimes even for each individual session. You can sometimes hire a third party or bring on a staff member (me) to do this for you, but then that adds to your overhead.
I'm in the middle of applying to clinical PhD programs now, but I am very glad to have witnessed the realities of private practice at such an early point in my career. As of right now, I'm interested in pursuing a joint research-clinical position with a VA medical center and research university or medical school, due largely to my own research and clinical interests, but also because of the single-payer VA system (no insurance companies to mess with). I could see myself operating a small, specialized practice (cash only) on the side, but based on my own experience, I'm not business minded or savvy enough to build a large practice from the ground up.