I think 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 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.
Second, 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 emphasises 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.