I highly disagree. Those consoles generally were just not up to par. The problem with those handhelds is they lacked the library you'd want, so you'd need a handheld AND a full blown console.There is no evidence to support this claim. The 3DS sold less than half of the DS. Vita sold less than a fifth of the PSP. Nintendo even had to emergency cut the price of the 3DS to help boost sales.
There has been a clear and significant downward trend in the sales of "handhelds" since the start of the iPhone era until the Switch came around.
They simply combined the sales of BOTH into one device. You can't look at it just as a handheld, you have to combine both of them. And the price-point is reasonable as well.