expect() doesn’t have a long history of precedence of having some other meaning. At least, I’ve never run across any usage of an expect() function before. This lack of semantic baggage is why it works well.
I still strongly disagree that assert() is right. I would rather stick with unwrap() if we can’t come up with a better name. I know that means that unwrap() on Option is fallable but is (presumably) not fallible elsewhere, but that hasn’t actually been a problem in practice with this particular function. Probably because the vast majority of unwrap() uses is for unwrapping an Option (or a Result), so the few times you unwrap something else you already know you’re working with a different type where it’s infallible.
I’d certainly like to have a different name that allows us to make the fallible nature of this API consistent, but assert() is not that name.
New suggestion: since unwrap() is usually used with Option/Result (AFAIK; I’d love to see some data on this), leave that alone. It’s a good name, it’s short, it doesn’t have the baggage of assert(), and variants work well for e.g. Result::unwrap_err().
Instead, rename unwrap() on other wrappers/cells to something like .into_inner() or .into_value(). Or maybe even just .inner(), which is nice and short and suggests that there is a single “inner” value that will be returned. Even better, it’s a name that’s not already used in the standard libraries (according to rustdoc search).