We went through this during a very stressful time when my SO found a lump in her breast, and it took the kindness of a nurse that worked between the doctors and the billing department to give us a possible list to get a ballpark of what to expect. She called us after hours to tell us because she didn't want to get in trouble with her manager.
Once we had that information, we called several hospitals for quotes and ended up being offered 40-70% discounts. It went from thousands to hundreds to ultimately having some of the tests comped... all because we had a little information and asked the right questions about the process.
This is a disgrace and not how you treat people's health.
However, a hospital could provide a list of prices that are commonly billed. What a list of prices would do is give you a sense if one hospital costs a lot more than another in general. If you knew you might change which hospital you go to and.. you know markets etc.
Of course it didn't cover every possible contingency... That's what an "estimate" means by definition. But that doesn't mean that it's impossible or even unreasonable to provide a baseline price, along with some of the more common events that can modify that price.
In my experience hospitals and surgery centers can't or won't tell you what something will cost up front.