Scroll bars weren't really "hidden", though; they were obviated.
At least on macOS, all the mouse-like input peripherals that Apple will sell you (both the Magic Mouse and Magic Trackpad), and all the inputs for their laptops, have two-finger "natural" scrolling.
Apple seems to expect/assume that you've scrolled a touchscreen at some point in your life (in fact, many people have scrolled more touchscreens than desktop computers at this point—including many old people!) and has built the OS around the idea that, just like on a touchscreen, scrolling is a gesture that you can attempt to apply anywhere, whether there's an affordance for it built into the app or not—i.e. that scrollability is a universal, system-level operation, not something up to the application. Every application in macOS/iOS is inherently built in terms of having some kind of "viewport" with a "document" loaded into it; and scrolling moves the "document" around within the "viewport." Even if that's a pointless thing to do, it still attempts to perform the operation.
(Though in terms of feedback, iOS has a more coherent responsivity to "attempted" scrolling than macOS does. You can "tug" at the top and bottom edges of the screen in pretty much any iOS app and get some extra out-of-document blank space, with a snapback when you let go. Whereas, in macOS apps, this only happens for "content" regions; whereas for "chrome" regions—e.g. the top-level icon listing in System Preferences—the region will only have snapback if the window is small enough for the region to be scrollable. If the window is large enough that everything is presented, your scroll gestures just go unacknowledged, as if the window wasn't a "document" in a "viewport" at all. Interestingly, you also can't resize such all-chrome windows; you only ever get a scrollbar on them if running on a computer with a too-low display resolution.)
What is missing, though, is a visual indication of whether scrolling will do anything, before you try it. Scrollbars used to help with this, yes. But the fix isn't simply reintroducing them. The world scrollbars were built for no longer exists: both web apps and modern native apps now do progressive loading/"infinite scroll", where the view-controller isn't necessarily aware of whether more content will be discovered when it tries to demand another chunk of data from its backend. Even when you force-enable the scrollbar, the size and relative position of the "scroll-thumb" now communicates no information about your "actual" scroll position in many apps.
As well, there are now real infinte-canvas apps (like Maps) where a scroll "position" wouldn't even be a coherent concept, because the document under the viewport is a self-connected torus. Universal gesture scrolling adapts well to this concept; scrollbars don't.
IMHO, I'd like to see a slight fade-to-black or 3D "bend away from camera" applied to the inner edges of the scrollable viewport, whenever the document in the viewport is not sitting flush with that edge of the viewport. This would provide a visual affordance of "scrollability" without providing any often-misleading information of relative scroll-position. Infinite-scroll documents would just always be "faded out" on all edges. Seems obvious?
> I don't really need the small sliver of menu space in PDF view to be reclaimed -- and for what, a "clean" look?
Nah, it's for shitty low-end laptops that still to this day have 1366x768 displays. Stick a title/tab bar, tool bar, and maybe an always-on bookmarks bar on top of the window, and an always-on start menu at the bottom, and you'll find that the PDF only gets about 400px of viewport real-estate. And now you want the PDF's own controls to steal more of that? There's a reason that Chrome first made the status bar into an overlay, and then merged the title bar with the status bar — it's trying to reclaim vertical space for exactly these constrained scenarios.