It's historically documented that our educational practices have come to us through a process of descent-with-modification, rather than having been rationally designed at some point to bring about abstract social aims or to achieve particular economic functions. Because of this, it's reasonable to expect that cultural evolution will be a much better suited than rational analysis as a framework for understanding the current structure of education.
The basic question is what insights into education can we get by applying the design stance (see Intentional Design) and reverse-engineering existing educational institutions. Just as with biological organisms, we can look at the system and ask: “What is this bit doing here? Why is it this way, and not some other way?” The assumption is, just as in the rational design model, that the various bits of the system work together to achieve a necessary function. Just as in the biological case, where the goal of evolution is individual fitness (survival and reproduction), the goal of cultural practices is cultural fitness (cultural survival and gain in mind share). While the ultimate test of cultural adaptive fitness is gain in mind share, cultural fitness does tend to be associated with economic productivity, technological innovation and military prowess, because these are the sorts of markers of success that people use to judge the success of a civilization when they are exploring whether to adopt a cultural practice.
What does cultural evolution contribute beyond what we would get from a historical approach? The main difference is the idea of Optimization and the expectation of a tendency toward increasing cultural fitness. Related to this is understanding the educational system as emerging from the social context, which acts on schools through economic and political forces. While there is appeal to the idea that education practices ought to be designed by experts, based on research about what works best, this is not how we got to where we are.
We shouldn't suppose decision-makers have properly understood what they undertook, either beforehand or afterwards. In particular, in many places and times parents have been responsible for choosing a teacher or school and paying for it. This gives parents considerable immediate power over schools, strongly encouraging schools to adopt practices that appeal to parents. When the government pays for school, then education is determined by a political process, which still depends on mass popular support (in a democracy). Whether the control is political or market-based, teachers have never had a free hand in determining how to teach.
Of course, the historical view also understands practices as being influenced by collective social forces such as economic demand. What the evolutionary view contributes is an explanation for how these mindless forces can result in any kind of satisfactory outcome at all. Cultural evolution leads us to see cultural change as being much more of a trial-and-error process than it is often seen to be. What ultimately matters about a cultural variant such as an educational practice is not the insights that led to it being devised or the marketing story used to sell it, but its ability to deliver culturally desirable outcomes. Since Prediction is Intractable, it's important to try lots of different things. Societies bring this about by having diverse practices. While it is important to have some sort of Story about the value of the practice, individual decisions are strongly influenced by the social environment. In particular, Conformity Bias leads us to follow common practices and Prestige Bias leads us to follow the choices of specific individuals who have high prestige or social status.
You can also look use evolution as a lens to look at the individual's interaction with the education system. Education provides a way to meet the individual's need to distinguish themselves, to demonstrate their own fitness. According to signalling theory, these displays need not be useful, and in fact are strongest when they have no practical value. You can look at the education system as having to satisfy the possibly conflicting needs of individuals to compete and the social need to support cooperation and productive work.
The evolutionary approach does have important weaknesses. In particular, it is possible to spin a great number of Just-So Stories about possible functions for aspects of an educational system, and it is often quite difficult to test these theories. In addition, these theories necessarily concern themselves with explaining why things are the way they are, and this is more suited to the needs of a political conservative (justifying the status quo) than the needs of a reformer (things ought to be some other way.) See Is vs. Ought and Evolutionary Politics.