And Baumol doesn't require salaries going up, it works just fine if salaries stay constant while the price of consumer goods goes down.
In both health care and education, the final customer often does not pay. When I go to a doctor and ask them how much something will cost, I get bewildered looks. They rarely hear that question. I don't pay, my insurance pays and I pay some co-pay. Same thing for education. I'm pretty much stuck with my local school district, or if its college, I get subsidized no questions asked student loans.
But compare that to something that's paid out of pocket by the consumer. Consider something like Lasik surgery. It costs about $2-3k per eye an. Pretty incredible considering its relatively new procedure. I can't find a single outpatient surgery covered by insurance that costs that little. Cosmetic surgery is similarly cheap. And the difference is that the Lasik surgery is paid by the consumer and most people would shop around, ask about prices, etc. No subsidized Lasik loans, no insurance coverage, just straight forward pricing.
I disagree. Healthcare isn't necessarily labor intensive. New technologies should make care cheaper. If anything labor efficiencies have made the actual labor required of medical care a lot less. Doctors used to make house calls and spend more time with you. Now you go into a doctor's office, wait up to an hour sometimes, sit in a room, have some lower paid aids take your vitals, get your information, etc and you end up seeing the doctor for 15 min. Doctors see about 20 patients a day and spend normally 15 minutes per patient. Compare that to 50 years ago and you can bet that there have been "labor efficiencies" since that time. That doesn't even account for tele-medicine for routine stuff like getting ear drops for a sick child.
As for education, teachers aren't paid a lot, all the new costs are administration. Education expenses did not grow proportionally to educator's salaries, but far exceeded them, so your theory doesn't hold up.
https://www.excel-medical.com/a-typical-primary-care-physici...