It really depends. I went without insurance for a couple years. I was able to bring every single price with the provider directly. As soon as I told them I wanted to pay cash in advance they had discount and other incentives.

In the end I paid less than even the inflated copay I would have had to pay with insurance. (And I had a lot of procedure and visit that year).

There is a good chance your 5-10k$ of copay would become 2-3k$ without insurance (Copay are absolutely inflated based on catalog prices that insurance negociate in the background).