What do you think about an official PSP emulator for PS4?

I think that one would be a great idea. Just patch in support for a second stick and render the games to 1080p.

The PSP has/had great library of games. The Vita TV is proof enough that there is interest.

But there is no interest in Vita TV.  It is a nightmare in terms of sales.

I think you mean PS Vita, not Vita TV.