Questions that don't have a goal which can be addressed should be closed. That is, if the question does not indicate what the OP expects from an answer, there is no way to provide a valid answer. If, on the other hand, the objective is for questions that ask a real, and complete question, yet do not explicitly state their future plans for use of the answers, that does not seem like a close worthy point on its own merit. There is no reason to create a custom close reason, however, for either version, if in fact it is closed. The in-built reason of Unclear what you are asking fits perfectly. Unfortunately, to my reasoning, the two questions you have selected do not fit in a group of questions that don't have a goal that we can address, or are, at best, poor exemplars.
The first question, Partner going through phone, does have a goal that I can identify. The OP explicitly states Am I in the right or in the wrong? Did I overreact? Does a partner have the 'right' to do this? If, by "goal" you are meaning what the OP wants from the relationship and you cannot, or will not, answer the stated question without that knowledge, then I think you're expecting some of the wrong things from this site. The answer to that question should not be motivated by OPs future plans. Either OP was right, or OP was wrong. Either the OP's partner does, or does not, have the right to inspect the phone. Conversely, if the OP had asked how to handle the situation, or what to do next, etc., then knowing OP's future plans would matter, and should be in the question, and without them the question is then "unclear" just as surely as one lacking regional context can be. As a side note, this question is worthy of closure. It is, in essence a poll question, and should be closed as such. While it is clear what the OP is asking, there is no criteria for evaluating answers, which are subjective, opinion-based answers.
For the second question, How to respond when told to "check your privilege", there is a goal, or future plan, given. The OP asks how to politely respond to such events. Obviously not for the two reported encounters, as they are now in the past, but as a guideline for possible future encounters. The OP even explicitly limited it to events involving random strangers. Furthermore, the OP even provided a possible response that had been considered, though not used, and has shown that some research was done beforehand. In my view, a good, on-topic question.
One extra note. A question shouldn't be judged worthy of closure based on the answers it receives. Sometimes users will ignore what the OP has explicitly requested, or rejected, and post their own "random" thoughts. Even when a cultural context is given some users will try to answer from their own, very different, cultural view. If the OP can be improved in an attempt to stem the flow of off base answers, that's well and good. Closing the question because of the answers, however, just isn't on, in my book.