Why is there less price transparency in some industries (especially healthcare) than in others?

To give a specific pair of contrasting examples:

• If I search for homes for sale in say Michigan, I can quickly see the listed price for each home. (See e.g. Zillow.) Sure, there might be taxes, commission, fees, discounts, etc., but the final price I pay will almost certainly be within ±50% of the listed price I see.
• But if I search for an assisted living or adult foster care home (for the elderly) also in Michigan, I am unable to find a single home that lists any price on its website, Facebook page, or anywhere else. Instead, every single home asks you to call or email them, or arrange for a tour. I have no idea what I'll have to pay, even very roughly, perhaps not even to an order of magnitude. I truly have no idea if the cost per month will be \$1,000, \$5,000, or \\$10,000.

Unfortunately, from my brief search, there doesn't seem to be much research by economists on this topic (but let me know if I'm mistaken).

Here are some possible explanations I've considered:

• Price transparency tends to be decreasing in price.

This might be generally true, but fails to explain why there is so much less price transparency in healthcare than in real estate.

• In healthcare, there is much more uncertainty and variation as to what each patient will end up costing.

But each healthcare facility does have standard rates for particular items, such as "a standard type X blood test", "a brain MRI in Machine #566", "a 24-hour stay on Bed #125", "a month's long stay in Room #351" (excluding all miscellaneous costs). Just like any restaurant or business has standard rates for particular goods and services.

The difference is that most restaurants and other businesses do publish these prices, while healthcare facilities do not.

Why is it advantageous for healthcare facilities to keep these prices shrouded in secrecy? Why have market forces not forced them to reveal these prices (in contrast to other industries)?

The US healthcare industry is perhaps exceptionally egregious. But I think it is also generally true in most countries that there tends to be much less price transparency in healthcare than most other industries. Why is this?

Please note that any successful explanation must explain why there is less price transparency in some industries (especially healthcare) than in others (real estate, airfare, food, cars, car repair, university tuition, etc.).