> But stuff like tab headers, buttons, or even text-sparse tiles - things meant for the user to click on - can, and usually should, prevent text selection. It is super annoying to be clicking back and forth through tabs only to have some text erroneously highlight and then stay that way.

No.

Outlook mail for example is full of your principle, which means copying a mail address becomes a «hover over the not-selectable mail address to pop up a contact card, scroll down the contact card to where the mail address shows up again, but is again unselectable, click the "copy to clipboard" icon»

Just make text selectable.