As a general rule, the Prime Directive makes perfect sense: your default instinct as Federation Personnel should be "do not interfere".
And, for 99% of space fleet officers, if it appears that there might be a reason not to interfere, thinking you should be interfering should be a "this is above my pay grade, calling starfleet" to get an admiral/Diplomat/Senator/whatever level of approval to explain the situation to and for them to make final decision on. Star trek communications seems to be in general fast enough that, in real life, you would be able to call a higher ranking individual to okay a breach of the Prime directive.
Of course, Star Trek is also somewhat inconsistent on exactly how easy it is to communicate with other people. And exploration craft which would be the ones to most commonly have to deal with prime directive questions (assumedly Federation space isn't littered with subwarp species between major developed worlds) might have more complicated communications difficulty.
There, the basic rule should also be "do not interfere", and we also then get into such things as the Enterprise having a, perhaps unrealistically eventful adventure (99.999999999% of planets with intelligent life would not be days away from disaster once discovered, given how they have to be stable for at least several 1,000 years to develop anything like a civilization). And even if the intelligent life is under threat, say a bad Ice age, most aren't "everyone is going to die in a week" but, well, maybe everyone will die in a year, or a 100 years, in which case there's plenty of time to call starfleet and let them send a team to study the situation for a couple of months, submit their minimal least interference plan to the Federation Senate, get it signed by the president, and implement the plan some 10 months after the problem was discovered.
Realistically, there should be 2-3 events where a captain needs to make the decision to break the Prime directive on the spot in the Entire history of starfleet.
So, its a perfectly sensible law for starfleet in a reasonable world where exceptions to the rule would be such absolutely rare occurrences that the advanced captain level text book would list in painstaking detail all 3 times an acceptable breaches of the Prime directive occurred, and probably then list a 100+ examples of times it was breached improperly, and why. Probably people breaking it for reasons that weren't time sensitive (yes, the plague was killing 1,000s a day, but even assuming the rate didn't slow we had 10 years to make a decision before extinction was a real risk) or wasn't actually a threat to the species survival (yes, the nuclear exchange would have killed a billion people if you didn't stop it, but there were 5 billion people on the planet and there was a near zero chance of imminent species extinction: that situation required setting up a listening post to track the progress of the war, not immediate interference).
Of course, In star Trek that one in a billion occurrence happened every year it seems, in which case less stringent rules seem sensible.