I made the mistake of trying the "Inbox" feature, and after going back Gmail started showing every email twice – once in a folder called "Inbox", and once in a folder called "All Mail". Both are, according to the settings, IMAP folders, and POP is disabled. But deleting an email in one of them has no effect on the other.
Every answer I've found so far (as well as the official Google help) says to "deselect all categories/labels to go back to your old inbox". However, the top checkbox (either "Primary" or "Inbox", depending on whether I'm trying the web interface or the Android app) is always grayed out, and deselecting all other categories does exactly nothing.
Fetching the mails via IMAP through a non-Google program (in my case, mutt) yields the expected result of every email showing up just once. Deleting an email in said program removes it from the "Inbox" folder, but not from the "All Mail" folder.
I have no filters enabled.
Is there anything I can do here besides switch to an email provider that doesn't try to (badly) predict my needs?
Edit: I'm talking about the standard Gmail web interface. The Android app does the same thing; I'd guess the reasons (whatever they may be) are the same.