[aithoughts]

Well, like you said, it really depends on what you'll be doing. Granted, there are different paths one's trajectory will take, and you won't know them in advance.

On the other hand though, I wouldn't presume to write my own cryptographic protocol without having the fundamentals myself. Wouldn't you say that it's actually reasonable to learn this on your own? There are so many options, paid, or free, that can help you with this. You could take a Coursera class, or follow an open source curriculum like someone said in the comments down below.

You did say "most individuals" struggle to learn in such a way, but the argument can be made that individuals studying cryptographic principles are not "most people", which, if not intelligence, shows a special kind of perseverence and dedication that will also differentiate them in self-study. I wouldn't say what you're saying is immediately obvious.

[Kalium]

You're right! The world contains a wondrous bounty of instructional materials the curious might use to attempt to edify themselves.

You're also right that the argument can be made that any individual who might seek self-study of advanced mathematics is not "most people" as I described previously. To that subject, let me offer a different formulation: most individuals attempting to study advanced mathematics independently struggle to learn effectively in such a way.

A non-zero number of people have set about doing what you describe with a special kind of perseverance and dedication... and wound up making rather severe mistakes. CryptoCat comes to mind. Perseverance and dedication failed to differentiate them. You may be different! It's very possible! But perseverance and dedication should not be confused for a rigorous and rigorously evaluated course of study. This becomes a significant difference when questions of scaling arise.

The world is full of options to help you learn, and I would not dissuade you from doing so. I just want you to be aware of the limitations likely to be imposed by a given educational approach.

[aithoughts]

As a percentage, how many US colleges would you say are excluded from the opportunities provided by "rigorous course of study"? Would you say you could get this kind of rigorous study at any university? If not, how many (as a percentage of all undergrad colleges)? Is this scalable/sustainable for the entire population?

[Kalium]

I don't know, and I don't think the answer is as relevant in this context as might be hoped. There are many known, admitted, and well-documented failings in and problems with the current tertiary educational system. Yet, it's perhaps possible that these are not repaired by stripping away some of the aspects that are of value.

The general need for a better approach might not be the same as a given different approach being better.