I'm probably biased because I'm from Europe but to me it seems that the decreasing cost effectiveness for health care and schooling in the USA is due to the capitalist philosophy that is so strong in USA politics.
For instance in health care, in the USA pharmaceutic companies have much more opportunity to sell or advertise their products directly to consumers. This is because as a consumer in the USA you have more influence in the choice of medicine or medical care you receive; as long as you are willing to pay for it, you can get almost anything. In many European countries it is not like that, it is many times the doctor who decides what is the most appropriate cure for you and even he can not always decide which medicine to use, many times this is regulated by the state or by health insurance companies.
In schooling there is a big competition in the USA between universities to have the best ratings; this competition drives up salaries of top professors to a level that does not reflect the extra benefits that they bring to their students. All of this can happen because universities are pretty much free to ask whatever fee they desire to students. Again in many European countries it is not like that, universities have only limited freedom to determine their tuition fees by themselves.
> pharmaceutic companies have much more opportunity to sell or advertise their products directly to consumers.
This is true, but I don't think its for the reasons you described. The cause is actually simply that they are legally allowed to advertise. I don't believe there's a single European country that allows pharmaceutical companies to advertise directly to consumers.
Consumers actually have a lot less choice than you'd imagine. You can request prescription medication from a doctor, but they won't necessarily prescribe it. Doctors can prescribe for off label usage, but the pharmaceutical companies are strictly forbidden from advertising that, and often even mentioning it. Doctors only really follow your request if its for an alternative treatment that they agree with. Similar to what you describe, insurance companies can also refuse to pay for drugs with generic alternatives, or request that the doctor follows other forms of treatment first.
Some of the advertising is to drive consumer choice, but it actually may be more for the doctor. Even if they don't prescribe a medication requested by the patient, they're forced to consider the drug, and they'll have the name in their head when reading journals and publications.
I don't think Professor's compensation makes up a big chunk of universities' spending. Administration seems to be the biggest and fastest growing cost.
I think that the pharma advertising, whatever the merits of the critique, is something of a distraction; remember, the cost absurdity is across the board. There's no direct-to-consumer saline-bag marketing, and yet it still has the $1-to-$700 blowup.
Also, I think the European model places excessive trust in doctors; I bet a lot of people there get stuck with some phone-it-in doctor who hasn't bothered to keep up with the cure that was found ten years ago, and the system still has to find some way to throttle all the demand to switch over to the good doctors that are diligent about this stuff.
With that said, I think the Europe-Asia vs US split is hint to the answer. Remember, Europe and Asian rail construction hasn't seen the cost blowup the the US has; theirs has kept in line with inflation a lot better.
Saline bags are $80/dozen. They used to be $25/dozen before the price increases. While manufacturers did increase prices in lockstep, they are limited by the ease of new entrants. You might end up paying $700 for a bag but that's the hospital setting the price.
India, which has actual capitalist medicine, has an extremely effective and cost efficient health care system. Scott Alexander even mentions this in the article.
I personally endorse the Indian medical system; everyone I know (including myself) who has a choice prefers to use it over any other system.
Primary schooling in the USA is not remotely capitalistic. There is no competition between schools. Similarly for transit construction; you get to ride whatever subway the MTA decides to build at whatever price they decide to pay for it. Similarly, capitalistic transportation system in the US (read: Uber + Lyft for people, Amazon + Walmart for materials) has been driving prices down.
Your "blame capitalism" theory doesn't really fit the facts.
For instance in health care, in the USA pharmaceutic companies have much more opportunity to sell or advertise their products directly to consumers. This is because as a consumer in the USA you have more influence in the choice of medicine or medical care you receive; as long as you are willing to pay for it, you can get almost anything. In many European countries it is not like that, it is many times the doctor who decides what is the most appropriate cure for you and even he can not always decide which medicine to use, many times this is regulated by the state or by health insurance companies.
In schooling there is a big competition in the USA between universities to have the best ratings; this competition drives up salaries of top professors to a level that does not reflect the extra benefits that they bring to their students. All of this can happen because universities are pretty much free to ask whatever fee they desire to students. Again in many European countries it is not like that, universities have only limited freedom to determine their tuition fees by themselves.