Is Golden mean or middle way possible in every situation?

no of course not.

Even great people use moderation in moderation.

No because it does not work for a binary situation.

If you are asking about the Aristotelian concept, then yes. But that’s because Aristotle’s notion of the golden mean or middle way does not mean what most people who are unfamiliar with the details think it means. For Aristotle, the golden mean is just a term for the virtuous action, and an action is virtuous insofar as it avoids the vices of excess and deficiency as much as possible. Thus it works just fine in a binary situation because you pick the option which is closest to the middle way, not a middle way between the two options (which is, ex hypothesi, impossible).

If you are not asking about the Aristotelian concept, then you would need to say more about what you are thinking. And if you’re thinking of something like the ad temperantiam fallacy, then finding the middle way isn’t even desirable in all circumstances (regardless of whether or not it’s possible).

^^ I was referring to Aristotle concept only and whether it can be useful in current situations.

I think it’s incredibly important to not run into the fallacy of the false compromise.

Think of King Solomon and the infant with two women claiming to be the mother. Offering to split the child in half is a false compromise – Two mothers, one baby, each mother gets half a baby.

A false solution, too, is naming the one who didn’t want to cut a baby in half as the true mother. The more competent mother, perhaps, but it calls into question whether that other woman isn’t batshit insane, no matter whose genes the infant actually had.