I don't agree that PS2 had better legs than the DS.
Nintendo easily could have sold the DS at $79.99 for example for several more years but they choked its shipments to peanuts on purpose.
If anything the DS was punished (just as the PS4) for having sales at a level too high that it was seen as a possible interfering factor for the 3DS.
Same thing with PS4 ... Sony doesn't want to sell PS4s, not because they couldn't sell them at $199.99 ... they could probably sell another 7-10 million PS4s at $199.99 ... but they refuse to offer consumers that option.
So is this actually an issue of "legs"? No it's not.
This isn't the case of the DS or PS4 not having market demand, if anything their death warrant is written because they definitely *could* sell several million units at a discounted price and Nintendo and Sony don't want people spending their money there. These systems are basically being punished for being basically stubbornly popular for too long.
If it was the case that the PS2 simply was more popular at age 9/10/11 for example and DS and PS4 simply could not sell even at a budget price by that time, sure I'd agree, but that isn't really the case if we're being honest.
This is why I think it's better to just compare like the relevant first 7-8 years of a product cycle. That tells you in better reality which system was actually more popular without interference or "we have to sell our next-gen systems" politics getting in the way.
You are probably right, here, for the most of the things. However again, all of those things are possibilities. The real results that happened, jugging only by themselves, PS2 stayed longer, and PS2 sold better. It could have been otherwise but it's not. So this is the reality and not the other way around. So we have to look at the reality, the things that actually happened, not what they could have been.