We are talking of SSDs on the order of 32GiB (maybe 64GiB) here. Not so costly in my opinion. In fact that's cheaper than putting a HDD in there.
As said: I'm pretty sure all nextgen consoles will have NAND on board instead of a HDD (and will require you to extand the storage with an external drive if you want more storage). Imho only the question remains if they will put a SSD controller to the NAND (I still assume Nintendo doesn't but we'll have to wait a few more days to know).