I'm not familiar with the etiquette here and I can't find the answer.
Would it be inappropriate to ask a vague "how would you improve this UX?" question presented along with a (easily accessible) working example? (Especially for web-based UIs)
Reviews are definitely a no-no. You need a specific pain point to focus on. You don't have to know what the solution is (that's why you're asking!), but you need to be asking a focused, specific question, ideally a question someone else might search/ask themselves. Questions are Too Localized when it's extremely unlikely anyone else could benefit from the problem; this is generally the case of vague "reviews" (they're also Not a Real Question due to vagueness in most cases).
Instead find something you know/think is a problem, and ask if there's a better way to do this specific thing. Answers should be focused and addressing the same issue. Another problem with "reviews" is 10 people might make 10, equally valid but totally unrelated points; that messes up the Question and Answer aspect of the site. Answers should be judged as solving the same problem.
Additionally, working examples sound great but the problem is if it's an external website, especially one you're intending to change, the example might go away when the website changes.
Questions on UX should be helpful for everyone in a similar situation, so it's important that questions both be generalizable and have permanent examples. Ideally post some screen shots and describe the problem, and maybe include a JSFiddle or similar in addition to persistent examples of the problem.