I don't need to care how it works, but you fail to understand my question: does it help find a ECDLP solution faster than the sqrt bound?

It has zero relevance that you can store lots and lots of keys, if at the end of the day it only works based on EC scalar multiplications. I hope you do realize that Kangaroo requires only a small fixed amount of multiplications, that is, simply the number of kangaroos for initial setup, and everything else is simple additions, which are hundreds/thousands of times faster than a point multiply? And it can solve a key, on average, in around 1.71 sqrt(N) operations (by operation, I mean addition, not multiplication)? Which is a lot less than what BSGS requires? It has zero squat relevance how well you optimize the storage, because the first thing that matters is how many EC operations are performed, not how many trillions of keys you can scan as visited or not. Because first, those trillion keys need to be computed one way or the other

It's like drawing on a sheet some mountains and saying - here's the world's mountains, but you actually need to climb them, not looking at a pretty picture. These are totally separate levels of magnitude we are talking about. But anyway, you answered my question. Which is a no. Case closed.