I doubt they will go above 1TB especially in the case of SSD. They will say if you want more storage then use USB devices. Which kind of makes sense because they have to keep the price as low as possible. And a lot of players already have all kinds of storage devices so they can use them with the next consoles, too. I think a 1TB SSD is the most we can expect.Storage is another thing which has me concerned about the upcoming consoles.
You're right, this amount is far too pitifully small for a console where you can't simply whack in a disc to install most of the game, then connect online to download the latest patches if you want to reinstall something you had to delete, in order to play it again. Obviously it's going to require expanding in order to have more than a handful of games installed at any given time. I can see it working for an ultra-casual market, but again, for that market you're also looking at dropping the price a bit more too, especially considering what the standard S offers for the same price.
But this storage issue potentially gets even worse next-gen. Especially with Sony's announcement of requiring an SSD to load the amount of data necessary for those 8k textures - here's the thing, we already saw the jump in install size from 1080p to 4k texture packs on the Pro and X, so that's even more storage per game, and even more time to download and install one, so even more incentive to add external storage.
I currently have 6TB of 7200rpm external storage in a USB3 RAID enclosure hooked up to my XBox, and I still regularly need to delete something I am still frequently playing when I buy something new. (And I have the luxury of most downloaded games taking 30m to install, hence how when a friend got a 2TB external HD, I downloaded all the games he wanted installed on it using my box here, because his home connection takes about 12 hours for each, and at my place it took a single afternoon to install 150 or so)
Getting the same amount of storage on a console which requires SSD storage to work would mean an additional £350 expense, and likely push the cost of expanding the storage higher than the cost of the console itself.