I was frustrated in this way during my math education, but lately my opinion about memorization has softened a bit.
The trick is that it has to be approached in the same way as in sports: Demonstrate a technique, explain the principles, attempt in live play, then return to drill muscle memory(now that the student has discovered how bad they are at it). Music is very similar - you can play a song badly, then drill scales and arpeggios a while, come back and suddenly you play the song better.
The point of memorizing is, in the end, to make the knowledge closer and more available to you. But there are several ways in which this cycle drops the ball during education and succumbs to rote learning as the sole factor:
* The teacher themselves doesn't understand the principle, and thus is poor both at explaining concepts and grading results. "You get a zero," they will shrug, when the student has misunderstood something and turns in a problem set with wrong answers.
* The principle isn't connected to "live play", making the technique unrelated to existing knowledge. It's the way in which education systemically fails most frequently, and it starts with having classes specialized per subject and limiting the crossover between them. All too often, all that happens is that you do some problem sets, get tested a little later, and that's it - and so all your focus as a student is on passing, not on learning.
* The drill focuses overly much on tricks and "gotchas" and not on developing confidence and long-term retention, making the student uncertain about how to generalize the technique to the tricks. In comparison, when I took judo, we drilled all techniques on one side only, for the entire semester. Is it useful to be able to mirror the techniques? Yes, but that doesn't mean that any study time needs to be allocated to it.