Please don't mark this as a dupe until you've read the entire question. Once you have, see here for why it isn't a duplicate.
This question was originally posted on superuser.stackexchange before someone pointed out there was no way to implement such a feature without doing it network-wide, and to post it here instead.
Let me start by saying that this feature strikes me as the single most common sense feature that could currently be implemented onto the network: the vast majority of SE's value comes not from its questions, but from its answers, and questions are just the vehicle that leads to them. Therefore, exceptional answers are far more likely to exist than exceptional questions are, and the vast majority of the time, when users favourite questions, they're doing so not because they want to come back to the question itself, but one of the answers to it.
Some have even dared to be visionaries and proposed more radical improvements (i.e. bringing the feature up to speed with the rest of the internet), and others have pointed out that the current implementation has serious flaws. In short, the best way to summarise users' outlook on these issues would be that, when it comes to the implementation of features that would greatly benefit its users, the SE network seems to have become stagnant, at best.
In this particular case, Jeff Atwood's official answer to this feature request came two years later, a slightly patronising (and heavily censured) response explaining how to bookmark an answer. In the comments to that answer, he provides the only reasoning that:
We believe existing in-browser bookmarking tools are sufficient for this case. Considering the average stack overflow question has maybe 3 answers, tops, the distinction between "I favorite this question" and "I favorite this answer" is minimal. Allowing favoriting answers would also make the interface noisier, and implicitly encourage questions with lots of answers. This isn't going to happen, so either come to terms with the decision, or find another site on the internet that's more to your liking.
Jeff is no longer a part of the network anymore, so we can live in hope that those currently at the top are less hard-headed about the issue, but that aside, his reasoning given in 2011 is demonstrably outdated: it's now common for questions on the SOFU sites - and even on the slightly less popular sites like English.SE - to attract between 5-10 answers, and for the more popular questions to attract in excess of 30. None of this seems to have been taken into consideration whenever users have asked for the feature to be implemented over the years - instead, these questions are robotically marked as duplicates, citing a 7-year old answer with outdated reasoning given by someone who's no longer involved in SE.
Even if for nothing else than to prove SE isn't determined to let itself stagnate and leave its users behind with the features of a site from the 2010s, when are we going to get the ability to favourite answers?