There are going to be people to buy just about anything when the price goes down.
Neither Wii U nor Xbone had the same kind of sales increase (not just at the cut point, but also in the following months) like 3ds.
Edit: looking for Gamecube sales, it doesn't seem that it found too many "people who are going to buy just about anything when the price goes down" despite numerous price cuts. I don't know if this is the best source for it, but I don't seem to find a quarter breakdown on Nintendo site:
http://vgsales.wikia.com/wiki/Nintendo_GameCube
Notice how not even the famous $99 price didn't move the needle too much.