I think the problem with the particular question that prompted this (this one I presume), is not so much that it is subjective, though it is, but that it is vague. The nature of any site built around Questions and Answers is that not every question will have only one answer. And indeed, some will have many reasonable solutions, and the choice between them is inherently subjective. The real problem comes, not just when a question is subjective, but when it is subjective, and also so open ended as to provide little value to someone who comes back and looks later.
In other words, "What Apps can't you live without" is a Big Question. So big that lots of people are just going to end up listing everything on their dock, and 'accepting' an answer is going to be meaningless. By contrast, "What is the best Twitter client for the iPhone?" or "What is the best media player for OS X?", while subjective, are sufficiently narrow, that the person asking the question can select a best answer, and while others might reasonably disagree with that choice, the question can be said to have a single answer for the person that asked it.