I wonder if there's a trade-off to this. On one hand you produce some really elite theoretical minds (Pontryagin, Lyapunov, Kolmogorov, etc.). But the counterfactual is that it excludes those with high IQ but are more practically-oriented as well as late-bloomers who didn't take to math early but would have become reasonable applied mathematicians (I belong to this category). I guess we will never know.
To draw a parallel, one of the criticisms of the French system -- where mathematics is treated as the most important arbiter of intelligence (for grandes ecoles admissions) -- is that other aptitudes are almost seen as secondary. It optimizes too much for a very narrow aptitude -- which is great for producing Fields Medalists, but underoptimizes for talent elsewhere.
In my experience, while the American education system on the other hand is kind of a piece of cake from K-12, it somehow manages to catch up at the college level (more or less). At the graduate level, the differences in ability between a U.S. graduate student and a Soviet-system/Eastern European educated one is largely diminished. And it does this without over-optimizing for any particular aptitude so deep expertise is developed over a broader field in the U.S.