Probably the "desktop" metaphor is irrelevant. I still have some physical papers I care about, but they are all holdovers from the 20th century, and I'm gradually tossing them in the recycle bin. None of my newly produced work is tied to a physical desk anymore. The "desktop" computer UI is no longer functioning as a metaphor because it no longer references anything meaningful. At this point, it's just bad UI, as you point out.
Our workspace is "the Internet," and the physical component of that is "the world." Some of us are homebodies anyway, but for those of us who like travel, sunlight, coffeeshops, coworking, etc., the solitary, at-home desktop metaphor is just wrong, because that's not where we store and recover information. We don't necessarily center our efforts around info we've personally created or hoarded, or, at least, we don't always think of ourselves as having created or hoarded it. We may not be looking for "our information" so much as "our group's information" or "the world's information."
That also leads to the question of what information is "private." As you pointed out, in a work meeting with a share-screen, it's embarrassing for everyone to see your messy desktop. Seeing all those "files" on a metaphorical "desktop" still implies socially (given what force the 20th-century desktop metaphor still has) that it's "private" information, which is part of the reason why it's embarrassing ("Hmm, what's in all those private files?"). But of course most of it probably isn't salacious; it's just evidence that we were reading something-or-other and "saved it to the Desktop." No weirder than keeping a full bookshelf of the books we've most recently opened.
(People who create less writing, art, etc. are often inherently curious/skeptical of the activities of those of us who generate lots of these types of files, but I think that's more of a social question than a UI question.)
We do want a way to separate personal and professional. Whatever my future UI is, if I search for yellow ballet leotards in my personal time at lunch hour, I don't want those product recommendations coming up on my share-screen at work that same afternoon. But imagining my UI as two giant desk drawers, one "at home" and the other "at work," isn't the correct metaphor anymore. That actually makes me expend more cognitive effort to imagine that I only have personal life in a "home" building and professional life in an "office" building, when that is no longer true. My wooden furniture is irrelevant. I want appropriate privacy safeguards on my information. I want privacy levels, like: "No one needs to see the modest dance leotard I haven't even bought yet. REALLY no one needs to see the SKIMPY leotard I DID buy for someone ELSE. The advance copy of my book, whose release date is next month, must absolutely not be leaked accidentally. It's OK if everyone in the office knows I was poking around the work-related information we all share, and it's great if they want to help edit my in-progress work drafts, as that gives us all more flexibility to get stuff done or take time off without having to 'ask for keys to the desk'."
