The nr. one thing any new OS should learn from the Amiga is its motto: "simple things should be easy, complex things should be possible." Not "Simple things should be possible, complex things should be Dark Souls"!
The next biggest thing would be the use of pervasive inter-process scripting. ARexx (I wouldn't choose it today but it worked) gave you amazing power to combine applications and automate various tasks - a bit like the Linux command line does, except it works everywhere. To illustrate, there was an ARexx script that combined a mail application with a chess playing game to create a chess-playing robot: you could mail it a board and it would make the next move, and mail it back. You could get two Amigas to play chess against each other, and thus avert nuclear annihilation.
"Screens", we would now call them virtual desktops, were way better than virtual desktops because applications are aware of them, and can be configured to run on a specific screen. Thus you don't waste time setting up new virtual desktops, moving windows across, etc., it's all automatic.
Assigns let you add globally valid short names for directories and devices. An assign can refer to multiple directories, and it can be deferred, meaning it is hidden until you refer to it. I really miss those on other OSes. Yes, you get links. No, they aren't the same. You don't have to create an assign in a location (they are always global), you don't need weird syntax for creating links, and you can delete them without fearing for your data.
The OS is essentially a microkernel that uses message passing for asynchronous communication, and that uses dynamically loaded drivers for things like devices and file systems. For modern usage you would really have to add memory protection (it wasn't available on the hardware of the time), and resource tracking (it wasn't finished in time for the Amiga launch).
And its culture was just different. The Amiga had so many small, simple productivity tools (it also lacked big, complex productivity tools, but that's another story). You had simple, yet powerful programming languages, music creation tools, drawing tools, etc. The tools of today are orders of magnitude better, but that power has come at the cost of considerable complexity. DPaint 2 can't hold a candle to the Gimp, but at least I knew how to draw lines with it. And is there even a single music creation tool for modern OSes that isn't either a sample arranger or a fullblown score editor?
So it can certainly be done. The question is, will you end up with the same joyful platform and the same joyful culture? I sort of doubt that: without a captain on that particular ship, odds are it will quickly turn into a Linux reskin. The world already has enough of those, and even if that weren't to happen, part of its magic was in the applications it ran. Just ports of existing Linux tools wouldn't have that. So I'd love to see a proper AmigaOS port to modern PC hardware, and it would totally rock - but I just can't see it gain the same momentum it had back in the day.