I have been following this phantasy for a long time (starting with the Atrix lapdock, continuing with the Nexus 4 running Ubuntu Touch and a SlimPort dongle, Nexus 5 and MaruOS and ...
Now I have a PinePhone and even made a few videos for YouTube (PeerTube, LBRY) demoing Phosh (the Phone Shell developed by Purism), Plasma Mobile and also Plasma Desktop and Gnome (the Mobile Shells have improved since, as they are still in early development). Honestly, Gnome and Plasma Desktop felt way better than their mobile counterparts. I think that this is not just familiarity, but also that they are made for the use case primarily.
It turns out that the UX affordances are sufficiently different between a small touchscreen and keyboard/mouse/monitor that the software has to look completely different. Attempting to get it to automatically adapt (Metro) is an even bigger stretch than responsive web design.
While it's quite possible that Apple will eventually release an iOS desktop, I don't think using the same device for both will ever work properly.
Also, quite a few people say they need 32/64 Gb of RAM, multiple high resolution monitors, large disks, huge graphics cards, etc. I don’t see a phone-sized device ever driving that, as needs will grow with hardware speed ups.
Now the software... I feel like it's being redone for the fourth time.
I haven't used this, but it seems similar to what you're asking about