Not cheap enough. Take any sized SSD drive you want and consider the price halved or even quartered by the next consoles, and you'll see either it's way too costly, or way too small. It'd only be viable as a local cache, like ReadyBoost, for either a performance enhancement over the standard system or as a cheap compromise for a system sacrificing RAM (so design; only difference is your take on it!). Flash isn't going to be a cheap alternative to an HDD in time for next gen's launch. Unless it's really late!
Wouldn't it be viable perhaps as a 16, 20, or even 32GB hard drive?
You could make this the low end "core" model, much better than a model like the Arcade with no built in HDD, yet you could be confident of flash prices falling for the whole generation.
Looking at newegg, I'm not sure these are analogous to what you'd need in a console drive, but USB flash drives run $32 for 16 GB and $65 for 32 GB.
I also recall before being told on B3D that while theyve stayed stagnant for a while (I know because I remember paying I think $25 for 16GB ages ago!), flash prices are due for a dropoff soon.
So at least 16GB seems almost feasible now, and if you reasonably got a 50% price decrease by next gen, much more so. And of course as I say, whatever the initial cost, you could expect it to fall more. So maybe if you started your "core" with 16GB, you could bump it to 32 later cheaply. Again, yeah that doesnt sound like much, but contrast it with the no memory in MS' first Cores, and it's worlds better at least.