> I must be missing something. Suppose I tell the provider I am going to pay them cash, directly; I will not use Medicare, Medicaid, or any other insurance. Are you saying that because said provider accepts Medicare/Medicaid for other patients, it is impossible for them to tell me ahead of time what they are going to charge me?
Yes. Medicare and Medicaid generally reimburse rates that are below COGS, so providers have to make up the difference with what they charge private insurers. If they didn't, they would literally go out of business - if you have to pay $100/unit wholesale to purchase a vaccine and Medicare only pays you $93 for the entire visit during which you administer the vaccine, you won't be around very long unless you can get private insurers to pay much more, to cover not only the $7 unit loss, but also enough to pay for all the overhead of running a practice (wages, office space, etc.)[0].
They'll make up the difference by requesting much more from private insurers, though they don't know a priori how much they'll get. In the end, private insurers typically peg their rates to multiples of what Medicare reimburses (for example: "we'll agree to pay 350% of Medicare's reimbursable rate for all reimbursable billing codes").
For various reasons (including both logistical and legal ones), they can't present one bill to private insurers and a different bill to self-paying patients. The amount that they'll accept to settle the bill may be dramatically less than the amount they bill for[1], but they can't provide different bills up-front.
So, any provider that accepts insurance is basically incapable of providing you in advance with a price quote that represents what you'll actually pay, regardless of whether or not you are actually on insurance.
In theory, providers who only accept a very small set of insurances and accept no Medicare patients would be able to do this. But in this day and age, you're almost never going to find one of those providers - the overhead of accepting insurance is large enough that it's to their advantage either to accept several different forms, or to refuse insurance altogether. And once you're taking insurance, you basically can't refuse Medicare patients (logistically and legally: some Medicare patients receive dual coverage or receive their Medicare coverage wholly under private plans, and you can't turn a patient away just because you discover that they're on Medicare if you're otherwise capable of accepting their insurance).
[0] These numbers are illustrative; Medicare (in aggregate) reimburses 7% less than costs.
[1] If you're insured, every time you visit the doctor, you probably receive an explanation of benefits statement, which shows that they were billed $1000, but their maximum reimbursable rate is $300, and they'll cover $250, so you're required to pay $50. The difference between $1000 and $300 is what I'm referring to here.