Bearing that in mind, also bearing in mind the number of times the Prime Directive was ignored, and since it is an interesting thought, what if the Prime Directive were the complete opposite of non-interference?
We have that already. It's called "white man's burden." History demonstrates the many reasons why this point of view is problematic, but for those of us who don't study history, I will summarize:
Except for in the broadest possible sense -- e.g. basic needs of food and shelter -- the definition of "help" hinges on the assumption that people from one culture can provide something that will improve the lives of people in another culture. This sounds good on paper, until you realize that more than half of the time what constitutes "improvement" is actually subjective. In the most egregious examples, we have the practice in colonial America of removing American Indian children from their families and placing them with white Christian parents on the assumption that being raised by good Christian foster parents would help to civilize them and eventually cure most of the social ills (plus all around heathenism) of the Indians. A similar justification was used for slavery, the idea being that black people were so culturally and mentally inferior that life as a slave was infinitely preferable to the sham of a life they would have "enjoyed" as a free man. When you consider this particular line of thought is still amazingly popular even today, you begin to see the problem: many times attempts to "help" others are misguided and/or based on ones own bad assumptions about what those people truly need.
You could, of course, try to limit yourself to a more objective assessment of their needs. Food and shelter, medical care, material support on an emergency basis, etc. This is less likely to lead to a situation of patronizing, but this too is not immune to the Law of Unintended Consequences. You may judge that a society experiencing a long term drought would benefit from you providing humanitarian aid, but the unintended consequence may be that this society decides not to invest in water collection infrastructure that would help it become self sufficient, instead transferring those resources to relatively wasteful irrigation projects and expecting continued aid to take up the slack. And even this is assuming you haven't accidentally tipped the power balance in a factional dispute by giving one sect or political party an unexpected surplus of resources just because they seemed to be more cooperative than their rivals.
The Prime Directive, however, is not incompatible with "Let me help." The underlying principal is that Starfleet will only help when they are asked to do so, and then only to the extent that the assistance has minimal long-term impact on the planet. This is why we have situations like the Volcano mission on Nibiru or Captain Georgiou digging a well on the desert planet. In both cases, their assistance wasn't a violation of the prime directive, only their making their presence and identities known to the natives in a way that strongly impacted their culture.
An even better example is that of Picard refusing to provide replacement parts to the Ornarans in "Symbiosis." It's an interesting choice, because it relies on a very direct interpretation of the Prime Directive. To wit: Picard understands that the situation is VERY bad for Ornara and should not be allowed to continue. But rules are rules: he's not allowed to interfere on their behalf, even if they -- indirectly or deliberately -- ask him to. On the other hand, he IS allowed to provide them with spare parts for their ships if they ask him to, since the Prime Directive doesn't actually preclude him engaging in fair trade or rendering assistance to people in need. He can, however, fall back to his "Well, we really can't interfere" justification even if he never actually explains to the Ornarans WHY giving them a plasma coil would constitute interference. They will probably figure it out eventually, and in doing so they will figure out what the Brekkians have been up to all this time. But -- and this is the important part -- they won't figure it out because of anything Starfleet did, and anything they decide to do about the situation will be a result of their own choices, and not choices that were made on their behalf.
And CHOICE is what it all boils down to. Starfleet will help people so long as it doesn't interfere with their right of self determination. Often times, that means helping people in such a way that they don't KNOW they're being helped, so their choices ultimately remain their own and they cannot be said to be influenced by any outside agenda. In the case of Ornara, this is quite a literal thing: refusing to give them the parts for their freighters is easily the most compassionate thing anyone has ever done for those people, but it'll be a generation or two before they figure that out, and in the mean time they're stuck having to clean up their own mess.
What if it was one of active intervention wherever and whenever needed or believed needed?
Starfleet would have a reputation for being a troop of meddlesome adventurers, constantly roaming around fucking with other people's lives, totally oblivious to the consequences of their actions. Picture all the chaos chased by Doctor Who's more interesting misfires and multiply that by ten thousand.
Pretty much every adventure show on TV is "Meet a stranger and help 'em out of a jam".
