Prior to the 360 & PS3 at least, how strong a system's legs are seems to have to do more with overall software support rather than pricing. The Wii had terrible legs, but that wasn't because it wasn't cheap. In 2011 it had its price reduced to $150, comparable to the PS2's cut to $130 in 2006 (and when you take inflation into account, it's actually much closer). What set the Wii apart from the PS2 wasn't price. It was games. The system had terrible long-term support, and even before the Wii U came out it was not getting many major releases. As a consequence, its legs were weaker than the PS2's:
We see the same thing with other systems. The N64 was actually doing better than the SNES in the U.S. early in its life, but it had weaker legs. By time it turned three years old it was already only $100, comparable to the $90 the SNES was by its third anniversary (and again about the same when you take inflation into account). Just like with the PS2 vs. Wii situation, the N64 had inferior long-term software support compared to the SNES, and that's almost certainly what caused this:
While the SNES continued to live on for a while after the N64 was released, the N64 died quickly once the GameCube was released.
Could the 360 & PS3 have had better legs if they had been cut to $200 by time the PS4 & XBO were released? Possibly, maybe even probably. Would they have been good legs? Not really. Would any potential boosts from such a price cut be enough to really be worth it from a business perspective? Probably not. In fact, I'd argue that the rapid shift away from the 360 & PS3 to full-on support of just the PS4 & XBO probably would have negated any effects of a price cut. Not only were the 360 & PS3 close to their absolute saturation points by the end of 2013, but the relative lack of post-next-gen support wasn't going to help things either. I don't see any case where the 360 & PS3 would still b doing well right now, regardless of how much they cost, and they probably wouldn't have done much better in 2012 & 2013 with additional price cuts, either. The PS2 was still getting games all the way up to 2013, seven years after the PS3 was released. There was no way in hell the PS3 & 360, after such a protracted generation, was going to get that kind of support after their replacements came out. After a certain point, price cuts just don't matter as much from a sales perspective, but long-term software support does. The delayed peaks of the 360 & PS3 essentially sealed their fates in regards to late-gen sales legs.
Oh software is definitely an important factor of the equation bit o think it's also a bit of a chicken and the egg style conundrum. I feel as though software support is a natural product of strong HW sales. When you look at the software support for the Wii and when it started falter it's clear that software declined as the sales fell. A similar arguement can be made for other systems as well. I'm of the mind that the increase in sales that would've accompanied regular price cuts would have led to continued software support for the 360 and PS3. Obviously I can't prove causation here with sales leading to software support butI do think the data suggests a strong correlation between the two it's just a matter of which you think is the driving factor. I believe it's HW sales and you believe it's Software sales. I believe it's the egg and you believe it's the chicken so to speak. We have no way of saying conclusively either way.