I understand about the PS4 not being PS3 compatible because the PS4 is not sufficiently powerful to emulate a complicated console like the PS3 but it really should be PS2 and PS1 compatible. No reason not to be if it can play audio cds and dvds.
All ps2's are ps1 compatible as are all ps3s. The PS4 is sufficiently powerful that it could fully upscale and anti-alias ps1 graphics no problem. I still have a dozen or so ps1 games and perhaps 2 dozen ps2 games.
Why would they let you play what you already own when they can charge you for the same game again? Nintendo does the same thing with VC.