Yes. Water systems, trash collection, fire departments, parks, etc. generally are cost-effective and well administered that they are typically excluded from these discussions.

K-12 is particular is an area where critics demean public systems, but where we have yet to see anyone scale an alternative at lower cost/higher quality targeting the same goals. (Apologies if someone has done it, I am not aware.)

Note: this means that systems that exclude classes of students do not count as they have different goals. Obviously, one could more cheaply build a private education system for rich kids who all have similar capabilities. But that is not the goal of public systems, who are tasked with educating the poor and rich, the deaf, the blind, those who speak other languages, etc. Generally, they are able to do this for less money per pupil than elite private schools that are not able to serve all students.

Anyway the point getting lost here is that states do subsidize public universities, but not as much as they did in prior decades. The debate you seem to be aiming toward is whether we should have public universities, to which I would say that we should have more of them, and they should cost students less by having taxes cover a larger share of those institutions.

Edit: I want to come back to this for a moment. Water and sewers are really core functions of public governments, and in the US they basically work near 100% of the time. They involve tremendous ongoing logistical work at timescales ranging from emergency pipe burst to capacity planning for decades in the future.

The notion that government involvement means poor/expensive service delivery is a fiction constructed from the outliers of government work.

> The debate you seem to be aiming toward is whether we should have public universities

Apologies if my argument came out that way. I agree with a need for public universities, I just disagree with the need to have them at any cost. Ad absurdium, a public university that costs $1,000 / $10,000 / $100,000 / $1,000,000 per student are all a good deal to a purist because hey, a need is a need.

The current system, however, incentivizes extracting maximum value for the stakeholders (administration) while delivering minimum results to customers (students). With a single-payer there's even a stronger incentive to inflate the operating costs.

If you went through US higher education, you've probably witnessed a few tricks designed for maximum revenue extraction.

* credits from one [cheaper] accredited institution are not transferable to another [expensive one], ensuring that you'd be subjected to a higher tuition

* courses that can be delivered online are not

* courses that are delivered online are paywalled to ensure only those who have registered and paid can view the precious content (something Open Courseware stood up against)

* there's no system where one can test out of pre-requisites by taking similar courses cheaper (or free) elsewhere. E.g., if you self-studied through some MIT or Stanford courses online, you still have to pay full tuition at Fill In The Blank State University

Granted, it's not always about effort duplication and resource waste. California Community Colleges, for instance, is good at centralizing student registration, identity management, and financials, so that each community college doesn't have to run a fully staffed department doing all that.

Ideally, though, an eager high school student should be able to

* load up on as many courses as they can manage online on their own schedule

* have an ability to test out of the courses for a fee that's lower than the full price of the course

* arrive at the university and pay full tuition for the courses that do require in-person training (nursing, medical sciences, any course requiring labs)

You're right, end of the day a public university is an extension of secondary school, but with higher concentrations of students (and hence fewer locations required and all sorts of economies of scale at play). There's no reason that grades 13-16 should cost more than grades K-12, so why do they?