Let's say we wipe the slate clean.
Universities are abolished, and after high school your grades are tallied and people seek out employment. If you slacked off during high school, well, have fun stocking shelves for the rest of your life. Not that there's anything wrong with that. You just don't have a choice because the rat race has been abolished! Huzzah!
Well, some people are fed up with stocking shelves and realize they made a huge mistake in high school. They desperately want to better themselves, so they begin thinking of ways to advertise their actual worth to employers.
Many of them realize that even though Universities have been abolished, they can still read textbooks on their own and teach themselves. So many of them do that, thinking they'll impress employers with their knowledge and appear desirable.
The employers say ok, prove to us that you're knowledgeable. Candidates tell them about all the textbooks they read. Employers say that's all well and good, but how do we know you're not lying?
The candidates leave dejected, but then realize if they only had a collection of domain experts to grade them on what they knew, they could then take those grades to the employers as proof of their intelligence!
The domain experts, who themselves are gainfully employed, say that they will administer the tests and help out with conceptual understanding on one condition: that they get paid, because hey, they need to make a living. Ok! Say the eager students....
See where this is going?
The rat race is an inherent feature of a free society. It can't be removed. If you try to abolish it in one form it will appear in some other form. Superficially the features of the rat race may be different but ultimately it will still be a rat race.
“At this point, one could object, ‘Though education teaches few practical skills, that hardly makes it wasteful. By your own admission, education serves a vital function: certifying the quality of labor. That’s useful, isn’t it?’ Indeed. However, this is a dangerous admission for the champion of education. If education merely certifies labor quality, society would be better off if we all got less. Think about it like this: A college degree now puts you in the top third of the education distribution, so employers who seek a top-third worker require this credential. Now imagine everyone with one fewer degree. In this world, employers in need of a top-third worker would require only a high school diploma. The quality of labor would be certified about as accurately as now—at a cost savings of four years of school per person.
[…]
Suppose you agree society would benefit if average education declined. Is this achievable? Verily. Government heavily subsidizes education. In 2011, U.S. federal, state, and local governments spent almost a trillion dollars on it. The simplest way to get less education, then, is to cut the subsidies. This would not eliminate wasteful signaling, but at least government would pour less gasoline on the fire.
The thought of education cuts horrifies most people because ‘we all benefit from education.’ I maintain their horror rests on what logicians call a fallacy of composition—the belief that what is true for a part must also be true for the whole. The classic example: You want a better view at a concert. What can you do? Stand up. Individually, standing works. What happens, though, if everyone copies you? Can everyone see better by standing? No way.”
Now the second paragraph. It's not clear that government spending cuts lowers general education. For instance, state governments have been lowering their support of public universities for a long time now, while tuition simultaneously has increased. Yet more and more people keep going to college. And taking out tremendous loans to do so! This is evidence that the draw of participating in the rat race is so strong that it can't really be stopped.
Of course most government spending on education consists of K-12 spending. If we eliminate public schools then either a permanent underclass that cannot participate in the rat race will be created, which has been a state of society in the past, or people will take out loans just to participate in k-12 education. That would put the poor at a bigger disadvantage than they are at now though. Is that what we want as a society?
So it's not really about "bettering us all" at the cost of enduring a rat race.
The dilemma is really between lowering government spending and accepting severely limited social mobility vs having a more inclusive rat race with more government spending.
