My main problem with it is that it is a zero tolerance policy where the outcome of following it is, rather than someone being expelled for bringing Tylenol to school, the extinction of a species with billions of lives.
I don't think you interpret the Prime Directive the way Gene Roddenberry did. The directive says that you don't meddle in the affairs of other cultures just because they act in a way that seems wrong to you (incidentally, that's why I am unimpressed with the reactions of all 3 species in Three Worlds Collide: all 3 are overly Yudkowskian in their interpretation of morality as objective). It does not say that you should not attempt to save them from a certain extinction or disaster, and there are several episodes where our brave heroes do just that. All the while trying to minimize their influence on the said cultures otherwise, admittedly with mixed results.
See the episode Pen Pals. The population is going to be destroyed by a geological collapse, and Picard decides that the Prime Directive requires they let everyone there die. Of course, by sheer luck they hear a girl call for help to Data while they are debating the issue, which Picard determines is a "plea for help" so doesn't violate the Prime Directive if they respond. But without that plea, they were going to let everyone die (even though they had the technological capability to save the world without anyone knowing they intervened). I believe...
Disclaimer: I am not a philosopher, so this post will likely seem amateurish to the subject matter experts.
LW is big on consequentialism, utilitarianism and other quantifiable ethics one can potentially program into a computer to make it provably friendly. However, I posit that most of us intuitively use virtue ethics, and not deontology or consequentialism. In other words, when judging one's actions we intuitively value the person's motivations over the rules they follow or the consequences of said actions. We may reevaluate our judgment later, based on laws and/or actual or expected usefulness, but the initial impulse still remains, even if overridden. To quote Casimir de Montrond, "Mistrust first impulses; they are nearly always good" (the quote is usually misattributed to Talleyrand).
Some examples:
I am not sure how to classify religious fanaticism (or other bigotry), but it seems to require a heavy dose of virtue ethics (feeling righteous), in addition to following the (deontological) tenets of whichever belief, with some consequentialism (for the greater good) mixed in.
When I try to introspect my own moral decisions (like whether to tell the truth, or to cheat on a test, or to drive over the speed limit), I can usually find a grain of virtue ethics inside. It might be followed or overridden, sometimes habitually, but it is always there. Can you?