uhm... a slim helped PS1 and PS2 in sales A LOT more than any other game did. The game may move hardware for 2 weeks or 1 month maximum, but price cut boost can last for more than a year
Again, software sells hardware.
Playstation 1 and 2 were successful only because of their powerful lineup, to begin with. A console with 0 good games worths $0.
Maybe a single sytem seller game's effect is more subtle, but it is there for many years, while the price cut is there until the counterpricecut.