Even if you set aside a dogmatic devotion to non-interference, practical considerations play an important role in when and how to intervene. A situation that would require the intervention of dozens of ships may simply not be a practical undertaking.Anwar's argument rings of "I'll only save you if it doesn't cost me time, money or resources; otherwise it is not worth saving you." It is a very self-centered attitude, not at all worthy of a society which places great value on sentient life, such as the United Federation of Planets.
That practicality may not even be cold self-interest. Based on what we've seen in Next Generation, humanitarian missions are fairly common for star ships. If a given ship is on a time-sensitive mission to deliver a vaccine to a planet where billions are threatened by a disease, the decision to continue that mission rather than divert to assist in the prevention of a natural disaster that would effect a planet whose population is in the millions is based on practical considerations.
Yes, I am being sarcastic. Whining about the responsability would make the Starfleet look silly and hypocritical - if you don't want to "play God", just stay away from all those other civilizations that you're afraid you'll influence. Or if you aren't gonna do that, just go out there and make tough decisions based on the reality of the situation, and decide if the PD applies and when it does not according to circumstances, and whether it should be better not to interfere or to interfere, and how. Which, oh yeah, is exactly what most of Trek captains have been doing all along.

