This has been possible for over a decade already. Sony has officially supported internal drive upgrades for every PS3 and PS4 model ever released. I upgraded my PS3 Slim (320GB) to 1TB, and both my PS4 (500GB) and PS4 Pro (1TB) to 2TB.
Changing the drive on a PS4 is literally the easiest hardware upgrade I've ever done; it takes less than five minutes.
That said, using an SSD in a PS4 doesn't seem to offer the kind of performance improvements that one might expect or hope for.
Right. I have an SSD in my PS4 Pro. Hitman on there doesn't load much better than on my 2TB Xbox One in spite of the SSD and PS4 Pro having SATA3. With that game, it could be partly due to the constant, unnecessary server connections, but whatever. Microsoft backtracked this gen by not allowing easy HDD swapping though, which is going to suck when the XB1 X launches in the few ones with 1TB instead of 2.