IMO, the Federation is wrong to interfere at all. Maybe warp drive is the wrong line, but we'll take it as a given for the argument. Pre-warp cultures should not be interfered with at all, especially not with duckblind missions that clearly fail or go wrong quite frequently. I accept that the Federation can identify pre-warp worlds and adopt them as protectorates so no one else interferes, but they can use hi-def probes to look at the world, and its people. Looking at the culture can wait until their ready.
Of course cultures shouldn't be interfered with, in the sense of imposed upon by force, but it's wrong to assume that any and all contact constitutes interference, or that a less advanced culture is somehow "not ready" for contact with outsiders. That's a grossly naive assumption that overlooks the fact that any single planet is going to have thousands of different cultures at different levels of advancement, and it's therefore quite routine in any culture's history to come into contact with cultures that introduce it to new ideas or advances. That's not contamination, it's natural, healthy cross-cultural interaction. The myth that you often hear is that "when two cultures at different advancement come into contact, the less advanced culture is invariably damaged/destroyed," but that's complete and utter BS. Half a millennium or so ago, a backward, isolated culture called Europe came into contact with the far more advanced technologies of the Mideast and Asia -- technologies such as gunpowder, the magnetic compass, the printing press, the lateen sail, and advanced metallurgical methods -- and far from being destroyed by the "interference," Europe was able to take this alien knowledge and use it to become prosperous and powerful.
The only times a less advanced culture has been destroyed (or nearly so) by a more advanced culture is when that more advanced culture is deliberately
trying to destroy it, or when it's unintentionally wiped out by imported diseases to which it has no immunity. It's never the result of exposure to new knowledge. Cultures are resilient, adaptable entities that cope with change all the time. Expose them to new knowledge and they'll keep what parts of it they're comfortable with, adapt what they can to fit their worldview, and ignore the rest.
That's the true purpose behind the Prime Directive, despite how it's been dumbed down and extremized in the 24th century. It's not "Don't make any contact with the primitives because they're too stupid and fragile to survive it," which is condescending crap. The idea is, "Don't tell other civilizations what to do or how to think. Don't try to make their decisions for them. If you must make contact, do so carefully and with respect for their right to believe and choose as they wish. Remember that your own judgment is imperfect, so don't assume you know better than they do." Avoiding contact altogether is the simplest way of doing that, but it isn't the only way and isn't always the right way; for instance, despite what 24th-century Starfleet says, it's insane and cruel to let a civilization die rather than make contact with it.