A practical (and sensible) reply to a 'I have tried everything' could be:
'I understand that having such an issue is frustrating. But please provide details about the things you have tried to solve this. In doing so you help us helping you.'
I think it is important to realize that this type of statement is to be understood as a rhetorical element, a figure of speech, so to say. The proper terminology would be hyperbole.
This rhetorical device is used more to express a personal impression towards a situation:
from the link above
it emphasizes, evokes strong feelings, and creates strong impressions. As a figure of speech, it is usually not meant to be taken literally.
I would thus argue to not take it literally.
The consequences are twofold:
First, the use of rhetorical elements in replies: Given that a hyperbole mostly is not to be understood literally, it is also not suitable to satisfy any requirements, like the requirement to document the attempts that were made to solve the question.
Thus the reply 'I've tried everything' is to be discarded when asking to document the attempts made to solve the question at hand. Such a reply only emphasizes the subjective impression that a lot of effort has gone into finding an answer, but does by no means describe what this effort consisted of.
Second, the presence of rhetorical elements in general within questions or answers: Here, maybe the question is more: Do we want to allow rhetorical elements within questions and answers?
If they are as obvious as the mentioned hyperboles I would say yes. However for other rhetorical devices or 'tone of voice', like sarcasm, I'm not so sure.