Rewritten in an attempt to better fit the format of a suggested practice
I would like to suggest that Yes, frame challenges should be accepted, but as with any other answer, they must be written in the spirit of providing helpful guidance to the asker - ParentingSE is not, after all a discussion forum.
My issues with current practice:
Unnecessarily broad ruling
An all-out ban on FC responses appears to either assume that such answers are inherently problematic, or that they are problematic to such an extent that we can afford to lose the would-be helpful FC's, both of which I think is false.
Due to the current practice, we don't have good data to base this discussion on. Only a very limited set of people have insight into all the FC's that have been deleted, and nobody has any idea of the number of helpful FC's that have simply not been written. Anecdotally, I have certainly refrained from answering questions with what I assume would have been helpful responses, knowing that they are of a kind that is not allowed here. I know there are workarounds and loopholes, but occasionally, the question is such that the threshold for participation becomes too high under the current ruling. The data we do have is from what the site looked like prior to these rules, but while I was not personally around at the time, my gut feeling is that the negative responses the rules put and end to were more noticeable than the positive responses we were missing out on, which is not necessarily to say we struck a desirable balance.
I hold that many times a frame challenge is the best response to a question, and that we cannot accept a practice that in many cases disallows the best answers. If we find that such responses are problem-prone, we must find a definition of the rules that targets the problem areas with greater specificity, and that will still permit the desirable responses.
Unrealistic expectations of site-specific knowledge
Current practice is that asker should clearly state if they accept out-of-premise responses, or the default assumption is that they don't. I think this is an inversion of both the asker-respondent dynamic, where askers will typically be less site-savvy than other users, and expecting them to know about key phrases to include in their answers is setting a high bar, and at odds with how FC's work: whenever the asker is aware of another view that might come up in responses, and is able to comment on that, is the area when we should expect FC responses to be least helpful. Indicative of a helpful FC is that the asker hasn't considered that there may be other approaches, and as such would think to comment on it.
The person who knows that they're asking about a hot-button discussion-prone issue, or the savvy user who is aware of other options but at the particular moment has a specific interest in one small niche area of a problem, and isn't investigating the bigger picture: these are the people who we can expect to explicitly state the boundaries of their questions, and identify which kinds of responses they don't want. I think it makes a lot more sense to default to all answers accepted, and expect those who aren't interested in that to say so.
It also appears to me that the current practice has arbitrary results, based on coincidental aspects of how the question is worded. For a question following the format "I cannot get my child to do X. Do you have any suggestions?", I have seen argued (by well initiated users) that an acceptable response would be (something tantamount to) "Ignore getting them to do X, it's not important", while such a response had been prohibited if the question had been "Do you have any suggestions for how to get my child to do X?"
I think the two example questions are functionally equivalent and should allow for the same responses. The fact that in one version, it is explicitly stated that the goal is to get the child to comply, whereas the former question is more open-ended, is coincidental. We cannot assume that that wording is the result of a deliberate judgment call by the original poster; that's not how language works.
I think that both requiring the knowledge of a magic phrase to explicitly allow FC responses, and the requirement of the asker to take extreme caution not to include any unnecessary assumptions into their problem statement is setting unreasonable expectations of the question asker.
The problem with asking permission in comments
A current workaround is to ask for clarification in comments on whether the asker accepts FC responses. I agree that this looks good enough on paper, but have had difficulties with this approach in practice.
A frame challenge is typically most helpful when it provides a new view that the asker has not at all conceived of. By nature, these require most explanations to ask about. A simple question in comments will bring to mind the type of FC's that are not generally helpful, so to be meningful, that comment will have to come with a lot of clarification. Typically, the new framing is the answer. The vast majority of times I've begun typing such a comment, I've abandoned it as I've found the comment to be a better fit as an answer than a comment, but also not allowed as an answer.
My suggested practice:
In my opinion, useful frame challenges are immensely valuable. Parents arrive at this page when what they're currently doing isn't working, and simply handing them new tools to keep down the same dysfunctional path will a lot of times only get you so far. As a collective, I absolutely believe we are at most helpful when we can affect the way a parent views a problematic parenting situation, in ways they wouldn't have conceived of. I think it would be a great loss for both the community and the parents (and by extension, their children) if such frame challenges were not duly appreciated here.
At the same time, we must recognize that ParentingSE is not a discussion forum, and that parenting is a deeply personal problem space. Crucially, we are not here to push our own agendas. It should not be important to the respondent that the asker adapt their values. To my mind, the hallmark of the kind of frame challenges we want to allow is that they help the parent fulfill their own values.
If the question is of the format "I need to get to Camelot fast. Do you have advice on the best pair of coconut halves, to mimic the sound of clappering horses?", you can challenge the minor premise as long as you honor the major premise. Thus, you'd be able to say "I don't know about coconut halves, but I know where you can find yourself an actual horse", but you wouldn't be able to say "Don't go to Camelot, it is a silly place."
I would also go as far as to say that the major premise doesn't have to be explicitly mentioned. Quite often, an underlying value is implied in the question, without being explicitly stated. If we can clearly see what problem the asker is trying to solve, I think we should be able to provide suggestions even if they are outside the scope that the asker has considered. The absolute majority of the time I expect this will be helpful. There may of course be instances where we miss the mark, and our particular answer is not of value to the poster, but there's a big step from that to saying the answer is offensive or that the poster might feel unwelcome.
There are plenty of ways to make a new user feel unwelcome. They should be dealt with, but I cannot see that as a problem inherent or endemic to FC's.