Recently Mxyzplk closed Are 5e Rangers competitive with other core classes? on the grounds that it was primarily opinion-based. If this is true, and BESW made a fairly convincing argument to me in Chat in support of its closing, then why are questions like The half-elf: is it balanced? & Sword-and-board balance in D&D still rolling around the site? Do we need to take a closer look at the questions using "balance" in the title and/or the balance?
The problem with balance questions isn't that they're "balance" questions: it's that far too often they don't meet other basic guidelines for good SE questions.
I voted to close Sword-and-Board as too broad--not as a balance question!--when you showed it to me in chat an hour ago, and it'd already gathered two more close votes to go with mine before you made this question. This means the system's working.
Both those questions are more than two years old, and the site's changed a lot since then. We don't actively go on witch-hunts to root out old questions which don't adhere to our newer standards, but whenever we notice them we smash 'em with hammers until they fit our ethos or turn to dust. You've brought two old questions to our attention which had previously escaped modern scrutiny and we're now evaluating them based on the site's current standards.
As for the specific questions at hand:
The ranger question is requesting a generic essay about a problem they've only heard of (not experienced themselves), and they leave the definition of "poweredness" as an exercise to the answerer. No answer could contain actionable advice for the querent, or even be sure it's relevant to the querent's vague theoretical scenario, so it's just an invitation to discussion. This is an appropriate reason to close a question on any topic.
I think the half-elf question is specific enough to fit our site's modern guidelines, not least because it's asking for actionable advice about a problem the querent is actually facing. Again, its being a balance question doesn't even come into the picture.
The Sword-and-Board question is so broad it's almost comical; it's requesting history and houserules across any edition of the franchise an answerer might feel compelled to draw upon, including editions where the topic isn't even valid! It should be closed as too broad and all-encompassing (again, the topic of balance doesn't have to be considered).
Most, but not all, balance questions are intrinsically opinion based.
Because balanced means different things to different people.
Two friends of mine were arguing about whether Mages from nWoD were balanced.
They both agreed that mages were more versatile than other templates, but generally less powerful at any given task for the same XP. That is there power was wider, not deeper.
Now one was arguing this mean mages were Weak -- after all they are less good at any task than another templated PC who was specialised. Thus they would never shine the brightest. The other argued that Mages were strong -- they are so versatile and that is what counts. They can interact with every scene, and can always contribute something.
So asking if Mages are balanced or not is a matter of opinion.
However, asking if Mages were more versatile than other WoD Templates, is a balance question, and is completely answerable. It is not in any way a matter of opinion.