I've been very busy lately but I want to share a short personal story that illustrates an important economic principle.
Last year our son started speech therapy with a highly-qualified and experienced pediatric speech therapist. She's really good with him and he has made tremendous progress over the last year. She was able to get us in within a couple of weeks of our first contact with her and he's been seeing her nearly every week since.
The speech therapist is paid through our health insurance, so we pay a specialist copay for each visit. After about six months of seeing her twice a week, we started feeling the pinch of what amounted to several hundred dollars per month in copays. Figuring that the school system would provide us with an equally-qualified speech therapist and considering that we already pay taxes to fund the school system, we thought we'd start sending our son to the local grade school for therapy.
It's been four months since we first contacted the school and he still hasn't seen a speech therapist there (he continues to see the other therapist). By contrast, our current therapist saw him in roughly 1/4 the time after our first contact. We've called the school a couple of times just to be sure they haven't forgotten us. They've assured us that we are "on the list" and that this is a typical wait time.
So where does economics come in? Prices function to ration scarce goods (in this case, speech therapy services) by providing market actors information about the value buyers place on goods and the costs suppliers incur to provide the good. This incentivizes producers to provide services that are more highly valued by consumers and incentivizes consumers to economize on services that are relatively costly.
Though health insurance markets are fraught with distortions (such as the dominance of the third-party payer system and anti-competitive policies in insurance markets), the fact that prices are allowed to function to some degree ensures that consumers directly bear the cost of their use of the service. As noted above, this incentivizes (however imperfectly) appropriate use of the service.
The public school system, on the other hand, doesn't allow for allocation by price. Since speech therapy services are scarce (i.e. they aren't infinitely and costlessly available to consumers), they still have to be allocated or rationed by some mechanism. In this case, that mechanism is waiting in line. While the administrators at the school could look at the length of the "line" to determine the degree of need for speech therapy services, the fact that consumers of the service don't pay for it directly implies that they have little incentive to economize on it.
The goal of providing speech therapy services publicly might be to lower the cost of speech therapy services, thereby ensuring access. However, as this example illustrates, the cost is simply borne in a different manner. Instead of an explicit cash payment, consumers bear the cost by waiting.