“It is the first polynomial time algorithm […]” only with important qualifiers that only matter for theoretical purposes. The paper is great and it’s important, but the algorithm itself is not used as even the most recent improvements are massively slower than the proof methods we were using in the mid 1990s.
The fundamental fact you note is cool, but was known to Leibniz. The cool part is that it took 300+ years to rigorously modify that exponential method into a polynomial time method. As noted, the actual AKS algorithm is a bit more complicated than that lemma.

]]>