In both OS X and Windows your desktop is just a folder with a background set to icon grid view. From right clicking to dragging, the UX is and should be identical to the file manager. So it makes sense to have that part of the UI handled by the program that's already a file browser.
Now a developer is going to recreate all of the features provided by Nautilus in a JavaScript and CSS extension. Any differences will make a janky experience for the end user.
Same thing with notification centers: another thing that both Mac and Windows added assuming it would be just as vital on the desktop as it was on phones. AFAICT they see very little use; I can't remember the last time I opened the notification center on either the Macs or PCs I use.
Not that new developments on the desktop aren't welcome, but widgets aren't it. Not every innovation that works on mobile can or should be brought to the desktop.
Certainly I use the PC one enough that I have the keyboard shortcut memorized and use it a bunch (Win+A). Interestingly, I find I often need it most in games, as the Windows version of the Xbox Guide, the Game Guide Bar, (even with the improvements in the recent April release), doesn't make it as easy to interact with things like Party Chat and Game Invite notifications as the Xbox Guide does on the Xbox One (where the Guide doubles as the Notification Center).
When I worked at a Linux distro (endlessos.com) they had modified Gnome to have a universal search bar on the desktop. It was targeted at a different group of users than me, but it seemed to make sense based on that group.
Hopefully Gnome does sufficient user testing to deliver a useful experience to some significant group.
Note that Active Desktop and ActiveX were not really related beyond being MS-powered internet technologies.
Honestly, I never use the desktop for anything so getting rid of it isn't a big deal to me. Could you explain what kind of things you use it for? What's so bad about viewing the desktop through a window?
So the desktop is a transition area, easily accessible, where I can put all the file I need for the task at hand right now. It's also the place I see everyday when logging it, so I can review what needs to be filed, and what need to be deleted. Clean desktop every morning, clean mind.
And it would fit their design philosophy to permanently remove it, which has been moving away from the concept of files as a whole. Instead, you're supposed to launch the app that does what you're trying to do and then open the file that you want to edit through that.
Another feature removal that has shown this direction, is the removal of the option to create an empty file from the context menu in the file manager.
Again, instead open the app that creates the type of file that you want and then create the new file in there.
They are removing the ability to have a Nautilus backed set of Desktop icons, with the intention of replacing this with something built in a more standard way for the rest of Gnome (which I think means web technologies?). As I understand it this not about removing desktop icons, it is about replacing unmaintained legacy code with more a modern alternative. I don't think the alternative is ready yet, but that's not to say that the direction they want to go is not having the feature.