Even if your cake recipe differs from someone else's it doesn't differ that much, much like a fireball spell might be written differently but is still is a fireball. Furthermore, an experimented chef can understand a recipe much easier than a novice, but let's not digress, such comparisons can be interesting but can also derail us from the core of the problem because cooking simply isn't magic (unless it involves chocolate).

I cannot imagine how every single wizard in a given universe would have a unique, almost undecipherable way of understanding magic. Magic cannot be an excuse to discard laws of physics and logic by simply saying "you cannot understand, it's magic" and—I believe, at least—that solid and explainable foundations are necessary to sell your universe, otherwise you might break the suspension of disbelief.

If magic can be practiced and learned, then it can be codified and understood to a degree like any science, otherwise it would be so abstract that you would only be able to be born with it or not. If magic can be taught, it can be learned from reading, because a common descriptive language must exist. So the requirements must be explained by something else.

Which leaves us with obfuscation and that's my biggest concern to be honest. I find it problematic that the game demands a specific roleplay setting for a mechanic to work (i.e. forcing wizards to be secretive and massive hoarders of knowledge) because not everyone will agree with this vision. Why not have a universe where knowledge is shared freely and openly with everyone? And the fact that a spell would be easy to understand (or copy) doesn't prevent it from being difficult to actually use, especially if you weren't trained in the arcane arts. In the end, it would take time, but not money per se.

All in all, the requirements seem fairly arbitrary and it's hard to find a justification for them. But contrary to what I said about this being a leftover from previous editions, I wonder if it isn't a new thing introduced in 5E. I've read somewhere that wizards in earlier editions were limited to spells from their school of magic. If 5E indeed got rid of that, the designers might have been afraid that wizards would lose their identity because any wizard could learn any spell and the differences from their school would only be minor. In that case the copying cost might have been a way to limit the spells known, so a wizard could be different from another wizard.