My first thought was that the mantra of "shut up and calculate" clearly means that we shouldn't get angry at the administrator for doing that. But Harry's conversations with Dumbledore seemed to go the opposite way. Dumbledore was trying to calculate how to do the most good even if some of the kids get hurt, and Harry was getting angry at him for it.
My guess now is that Harry's not angry at the administrator for calculating. He's angry at the administrator for not calculating how to parley a million dollars into a kidney and a bunch of equipment, salaries, et cetera, and a breakthrough cancer treatment as long as you're spending money, anyway. And that, I presume, is what the "Cheating" subtitle on the prelude means.
One thing you've left out of the analysis is the cost of the signal. An ivy league degree may or may not be mostly signal, but either way, very few low status people will be able to get one.
So, one way that signals can lose their meaning is if the cost drops. Take the example of buying a drink. If drinks are expensive, then buying drinks for women you don't know is a costly signal. (Note that there's an equilibrium here; the more successful the tactic becomes, the less costly the signal becomes.) As we all become wealthier and the relative price of drinks goes down, the statement being made about disposable income goes away, and it becomes just a ritual.
I would say, then, that the primary driver for a signal to expire is not for it to be common knowledge that it's a signal, but for it to be common knowledge that it's a cheap signal. Knowing which signals to pay attention to reduces to the question of accurately estimating how costly it is.
Unless you're going to cloister your children until the state forces you to release them into the world, they're going to encounter plenty of irrationality without your needing to deliberately lie to them. I would try leading by example, rather than hoping for an epiphany that may never come.
It suddenly occurs to me that Dumbledore has seen two interactions between Harry and a Dementor. In the first one, it almost destroys him. In the second, he casts a Patronus that destroys it. Neither would seem to provide the kind of evidence that you would need to confidently assume that other Dementors would run away from you if you said "Boo" to them.
So, is this enough evidence for Dumbledore to decide that he's wrong about who broke Bellatrix Black out of Azkaban?