Insurance Claim cost for a claim is significantly higher than “no insurance” cost

Hello all, need some advice: I had genetic testing done. I was led to believe the cost would be $200 which I thought was reasonable. 6 months after the service was performed, I was given a bill for $3,000. The claim was sent to my medical insurance company and the cost breakdown was $6,000 minus a 3,000 “insurance discount” which leaves me with $3,000 out of pocket.

I called the testing center directly and they said the bill was correct and I owe $3,000. They have a special rate for NOT using insurance and that rate is $200 (instead of 3000) which I would been able to get if my doctor did not process my claim through insurance.

Main question: If I would have known that special rate of not using insurance for $200, I would have gone that route. Now that the insurance claim has been processed, is there any way I can go back and have the company reprocess the procedure as the “non insurance” rate? (Note I called the service provider and asked and they said no). It just seems odd I have to pay SIGNIFICANTLY higher (1,500%) out of pocket for having insurance.

An answer and general helpful thoughts would be appreciated, thank you.