It's very likely going to be some type of hybrid system. Even 1tb SSD drives retail at around £100. Yeah Sony will get them much cheaper but that's still a decent chunk of cost built into a system imo.
They won't be selling these things at a loss.
I think you're wrong on both points there. Both PS3 and PS4 were initially sold at a loss. Money is made back from PS+ subscriptions and games.
And it's likely the drive will be 1TB SSD with no HDD. There's no way a gaming system can keep copying stuff from SSD to HDD to SSD without some kind of performance penalty.
What if I decided to play Title A which is installed on the HDD. "Please wait whilst we get this game ready for you." The game starts copying essential files from HDD to SSD which make take a couple of minutes. That's a couple of minutes too long.
Then after five minutes of playing Title A, I find it a bit boring and decide to play Title B which is also on the HDD. So Title A has to be copied back from SSD to HDD and Title B from HDD to SSD. This is going to take what seems like forever.
It's probably going to be some kind of flash memory soldered on to the motherboard because it's going to be faster than any current solution available on PC (maybe using PCI Express 4.0 or even a custom solution).
How you get extra space, I have no idea. If you could plug in an external hard drive, then maybe you will have to go through that rigmarole of copying stuff to the internal drive before you can play something.