I'm guessing you're referring to the fx series? All of which were severely outdated within 2 years of release? Not to mention you're forgetting the fact that the PS4 and its OS are much more lightweight freeing up headroom for other tasks. Dolphin is definitely possible. Even then you're looking at mid tier performance (at best)
Oh yeah it's possible, but with out Direct X or Vulcan your left with hand coding a lot of that stuff since your not dealing with "overhead" some of that overhead is super nice drivers and Direct X and Vulcan.
and yeah FX CPU on my machine that would compare favorably to the CPU in the PS4 "The PS4's CPU is roughly equivalent to an FX8120 underclocked to ~1.8GHz." grabbed that from another web page but it's true. The PS4's CPU is super weak compared to a PC. Windows isn't eating up over 3Ghz of resources by itself on a multi core CPU (I also have more RAM than the PS4 in my machine so it gets worse and worse.)
My main machine is a Skylake i5 OCed to about 5Ghz my media center PC is an FX 6200 OCed to 5Ghz, 16GB's of RAM on my main machine 10GB's of RAM on the living room machine with 4GB's of GDDR5 VRAM on both of those.
Sorry it might be possible but your never going to see anything running all that great on it, expect like Shield TV levels of performance on the PS4 in regards to emulation. Many emulators will run perfectly N64 PS1 and feature lots of enhancements if someone can get the ported over correctly. Anything newer than that is going to require herculean levels of work.
Edit: Basically it all breaks down to this "I'm guessing you're referring to the fx series? All of which were severely outdated within 2 years of release?" Yes except running much slower... If that doesn't put things into perspective in regards to what is possible on the PS4 nothing will.