> But by archiving the email, the email disappears from the list, which already implies the action was successful.
> In this example, the button already includes a confirmation so the toast is entirely unnecessary.
I vehemently disagree with the idea that just because you're already communicating something one way it's bad UX to include another way of communicating the same thing at the same time. Redundancy in communication is a feature, not a bug, and it's present in all human languages. It ensures that even in less than ideal conditions the message still gets through.
In the case of toasts, having a single, standardized way of communicating the status of all actions (and if possible providing the undo) allows a user to quickly pick up on the pattern. Extra indicators closer to the action can be valuable too, but it's when they're paired with the toast that their meaning becomes entirely clear. To remove the toast in favor of a bunch of specific indicators is to force your user to learn several different ways of saying "it's done now" entirely from context (many of which will be small and subtle as in the examples given). This might work fine for you and me but isn't great for, say, the elderly or the vision impaired or children.
Unless they're actually getting in the way, toasts aren't bad UX, they're redundant UX, and a UX designer shouldn't be striving to optimize away redundancy.