I don't think Dolphin would work on any home consoles, even the Shield TV barely runs Dolphin and only some games run at what I would call playable speeds. The Shield TV is the same hardware as the Switch just 1GB less RAM but with a faster CPU and GPU...
Comparing the PS4/Xbox One to a PC, what will trip things up again is the CPU speed, the PS4 and Xbox One both use AMD's older CPU/APU things... they kind of suck at IPC and I run Dolphin on an AMD CPU in my living room similar to what would be in the Xbox One or PS4 except mine is 6 cores clocked at near 5Ghz... Dolphin runs great except my PC's CPU is running nearly double the speed of the PS4's CPU and then there is the whole other situation that the APU's used in the home consoles are like cut down versions of the PC CPU's... So even less performance clock for clock.
GPU wise the consoles do great, in fact for games designed for the systems the CPU is not holding anything back, it's when you try to hit emulation where things get CPU intensive the home consoles really have a weakness.
In my estimation it could be possible to do Dolphin or PCSX2 on the home consoles, but it's going to be a LOT hard work. I just don't see anything much beyond proof of concept work if it happens at all.