Please consider accepting a good answer, even if it does not (possibly) give you what you asked for
I have to say I completely disagree with this. Accepting an answer is saying that that answer solved the OP's issue. If no answer solves it, then none should be accepted. Sure, it would be nice to get that extra 15 rep that comes with an accept but, as the OP, you have every right to wait for a better answer. You have the right, so to speak, to hope.
This is not (only) for the sake of the answers, given to this question. Acting this way, you make people not want to answer this kind of questions at all.
I'm sorry but if someone's only answering to get the 15 reputation granted by the OP's accepting their answer, they are here for the wrong reasons. Even putting aside the lofty sentiments about providing knowledge for the sake of knowledge, helping the community, providing answers for future generations etc., even ignoring all that and treating this entire site as nothing but a game where the sole objective is amassing Useless Internet Points©, even then, a measly 2 upvotes give more rep than the accept. I really don't see why the accept is such a huge motivator. We answer because we want to help people and/or because we want the reps. Well, the reps will come whether our answer is accepted or not.
Eternally unanswered questions are a pain on the site, so:
Do not confuse "answered" questions with "questions with an accepted answer". A question counts as "answered" if it has either i) an accepted answer or ii) at least one upvoted answer. Accepting an answer is nothing more than the OP saying "this solved it for me". It doesn't mean the answer is The Answer®, it doesn't mean it's better than the other answers, it doesn't really mean anything at all. As explained in the relevant SE blog post (emphasis from the original):
This is a simple social convention we use to close the loop between the person asking and the person answering -- with a little reputation sugar to sweeten the deal (+15 to the answer, and +2 to the owner). Accepting an answer is not meant to be a definitive and final statement indicating that the question has now been answered perfectly. Heck, we don't even expect people asking questions to come back and accept an answer most of the time.
Finally, to illustrate your point here, you are using answers that were posted two days ago! Good grief, even if the OP had received the best possible answer, the answer of their dreams that made all their wishes come true, they still would be justified in waiting a few more days in case anything better came along before accepting.
So, no, if an answer doesn't give you what you want, there is no reason to accept it. If it can tell you definitively that what you're asking is 100% impossible, you can indeed think about accepting it if you wish. However, there is never any pressure to do so. We all (or, at least, I do) often leave comments asking the OP to accept an answer if it solved their issue. Those are more to educate the OP than anything else though. Yes, accepting is good since it sometimes makes it easier to find the best answer but no, it is not essential to the working of the SE sites.