I don't want the process of getting healthcare to be as adversarial as customer support. People will be dead by the time anyone answers.
Need an ambulance? Let me escalate to the department that will escalate you to a department that will dispatch the ambulance in 5-10 business days.
Tell me you've never needed significant healthcare without telling me.
It's never about "ambulances". The bureaucracy will happily call an ambulance for you, as it ends their involvement and absolves them of liability. And the ambulance company is happy to show up, as it's a large billable event. In fact when seeking/obtaining complex medical care, this is one of the failure modes you have to constantly swat away!
As for interacting with the bureaucracy to obtain real care, it's gotten to the point where it's easier to get something done calling a bank. Navigating the medical bureaucracy is probably on the level of calling Comcast-Warner (although I haven't had the misfortune of having to deal with them for a decade, so I'm sure they've gotten worse as well).
Even before "AI", my standard experience is a multi-level phone tree, multiple mandatory announcements before you can even proceed, then waiting on hold. That merely gets you to an answering service who types a ticket into the computer system. Then you wait a ~day for a nurse to call you back (if you miss answering this call, return to step 1). Then the only urgent appointments are invariably with "nurse practitioners" who throw pre-canned advice at you, as they don't really know what they're doing. That's four layers running interference to keep you away from an actual doctor, who you will finally get to see in a month for a fifteen minute appointment, if you are lucky.
I have already given up the idea of getting heath care. I have top-shelf insurance that has all the preventative stuff included, but it is simply not worth the effort. The quality of care is not even worth my co-pay.