I'm not sure that's a simple argument and can't imagine many would agree.

Undergrads who do research generally aren't very good at research yet. A major reason is they either lack or don't fully understand the pre-reqs, which they progressively and cumulatively learn during undergrad. A student can be incredibly smart, but acquiring a strong rigorous math background will still take years.

About pre-reqs: third and fourth year PureMath classes at UofWaterloo consisted of math I already took in HighSchool in Romania: group theory, ring theory. Plus some calculus I already read in high school out of curiosity: measure theory and the Lebesgue integral. Another Romanian guy at UofW was auditing 4th year classes while in his first year (he is now a math professor at an American university)

I can see a committed and gifted student being able to get most of the pre-reqs for doctoral studies in America or Canada while in high school.

Working on that skill and ability is the entire point of postgrad. If those are the skills you're working on then you should be in a postgrad program.

If you don't know the foundations well, you don't belong in a postgrad program. That's the reality and how it currently works. Undergrad teaches you those foundations.

Anyone can try doing research, even undergrads who half-know the foundations. However, trying research doesn't mean you have the background to do great research or to succeed in a postgrad program.

Let me ammend my statement. *"Anyone who succeeds at publishing research deserves to be in a postgrad program."

Plenty of people in postgrad programs don't know the foundations. It's ok. You are there to learn.

Completely unfair to expect someone already doing research to slog out 4yrs of classes not furthering their career.

You can definitely do research in an area without having a good background on other topics.

People sometimes accidentally do research. I'm not joking.