I'll be going back and updating the original post over time (it's permanently linked in the Help Pages menu above), but I wanted to answer a few of the questions that have come up.
First, what if Amazon "empties the trash". Although it's possible (for that matter, it's possible Amazon would cease to exist, which would be much worse), they never have in the past and the prompt when you put something "into trash" tells you that you can "always" go back and restore it to your collection. It's still a part of your Kindle account, which the kindle.amazon.com site knows (it ignores that something has been moved to trash) and which I suspect any Amazon support person could check, if they had the order number (one reason I archive all my Amazon receipts). In the end, we have to trust Amazon to do what the say they will (including never deleting a book from our archives at their end).
Second, why doesn't it disappear from your archive right away? That's because the physical Kindle devices actually keep an record, in memory, of your archives. When they check in (sync), they only download the "new" books (and each Kindle knows where they left off in checking). However, if you do a RESTART (don't do a full "factory restart" or you'll end up with a Kindle with no documents/books on it and will have to reload what you were reading), then the archive listing is wiped (oddly, the reboot issue caused by too large an archive doesn't always work like a restart, as the archive list isn't wiped every time, from what i can see). So, when I first checked my Kindle (K3), it still had a very high number of books on it (just not all of them, nor low enough to reflect the ones I had moved to the trash). I did a RESTART using the menus (I don't know that doing so with the on/off switch wipes the file, but suspect it does). As soon as it booted up, my archives were at 0. I opened the archive, waited a bit and it had loaded 3431 book & audiobook titles (I suspect anything over this initial "big gulp" number is what causes the rebooting issue). After a while, it worked its way up to 6713 and stayed there - that was the current number of items in my library (including Audible books) that were not in the trash. I've searched on a rather oddly titled book from my library that is in the trash and it can't be found in the archives now.
When I checked my Kindle Fire, the only way I can figure out to wipe the old archive listings is to do a factory reset (definitely not what I want to do) or to clear all the application data from the Kindle Keyboard app (again, don't want to do that, until I back up what is on it, so it can be easily reloaded, assuming that works). For a kid's Kindle Fire, though, either wiping the app data or keeping them blocked from WiFi except during designated times (then, purchase, download, then "trash" items while they are blocked) might work. On the Fire, too, there are starting to be a few parental control apps and I believe at least one lets you designate exactly which books are viewable.
Third, there are some other ways to manage (and back up) your books and I plan on a post about that, as well. I (like some of you) use Calibre (although not all of its features) as a part of this plan. You don't have to remove any DRM, either, as all you are wanting to do is to keep track of your books, be able to add tags (more powerful than collections, but essentially then same idea), make notes, track what you've read (or want to read next) and be able to search on any of that. In other words, take the features of the MYK page, the Media Library, the Kindle itself and the kindle.amazon.com pages, roll them all together and add even more functions (what we all expected Amazon to do in the first place, as if they had, Calibre would not be nearly as popular with those who only buy Amazon books).
Fourth, can you still tell that you have purchased a book at Amazon? The answer is yes, you still see the prompt that you have already purchased a book on the details page, just as you do now, provided that you are not looking at a new edition (with a new ASIN). If it is a new edition (not as big an issue with most indies, but can be with some big 6 publishers), you won't be prompted. Instead of then checking the Manage My Kindle page (which was usually my next step), you'll check in your Media Library instead (so, just bookmark the page). Do a quick search in the Kindle books view, then open the trash and search again. Or, stay tuned for a way to manage all your books (including those not from Amazon) in Calibre, so you can search once, there.
Last, even those who don't want to hide their books can benefit from using the trash, provided their library archives are of any size at all, even those too small to cause reboots. You don't want to keep all the books you have on your Kindle, simply because it slows down accessing the home page (especially with collections). The directory system used by the internal memory has some technical limitations. Once you get a couple of thousand files in a single directory, it starts slowing down a bit. That's only 400 books, if you have all of the extensions for each one. At a thousand books, you'll definitely start seeing the effects, with long pauses after hitting the home page. The archives can be larger before you see a problem, as that seems to be kept in a single file, but as its size grows, you start seeing pauses there (and rebooting). So, if you can't keep all your books on the Kindle or even all of your unread books, even a small library can start having organization issues. One thing you can do is to hide the books you've read (not a good idea for those of us that read a LOT and can't remember if we've bought a book we've just run across in a used bookstore, but, then again, that's not as much of an issue here, anymore, as we don't go as often ... I definitely don't "need" many books from there and ours has started only accepting paperbacks except for absolutely new releases, so isn't even a good place to track down a hardback of a book I want to keep on the shelves).
What I wish Amazon would do, though, is hire a programmer to merge what they started at kindle.amazon.com (which is very basic and primitive) back to the media library (and enable all the features there). It was the perfect spot to then upload the changes from your Kindle, as it already supported tags (which is all that collections are) and ratings (the rating you do on your Kindle doesn't appear to update anywhere at Amazon, so there isn't any point in using that feature, that I can tell) and sharing out (or not) your collection contents with others. Instead, we have been given multiple places (three just at Amazon, plus on the Kindle or apps) to perform the same functions and none of them are integrated together, not even their own social media site for books (Shelfari, which also doesn't work well for "large" libraries, with large being even a couple of hundred, there).