[Haftdrarp]

If no one suffers from the 3 poisons of greed, hatred and delusion then how would these problems arise? Also, yes sitting on a cushion will help solve the worlds problems due to what I said above. That's probably true but it's pretty close to being a tautology: if people were perfect, they would act perfectly. Well, yes. And? They're not and they don't. And in any foreseeable human future, they're never going to be.

From my (extremely poor) knowledge of the Buddhist texts, I think you're probably right that there is not much evidence of Buddha's social engagement. But he lived in an iron age society. Is it sensible to use his interactions with iron age social structures and his assumptions about governance and society as the model for our own? That seems like madness. On the other hand, a commitment to reducing the suffering of others seems like a pretty natural and obvious corollary to accepting the core Buddhist teachings - I don't think one has to limit ones understanding of the dhamma to what is explicitly stated in the texts (and nor, in very changed circumstances, do we have to adhere blindly to what is in the texts). As you say "Buddhism has adapted to whatever culture it is in" so, given the fact that our societies are so radically different to the Buddha's, why can't we extend or adapt Buddhism to reflect those changes?

The Mission of the Church is found in Mark 16:15 "He said to them, "Go into all the world and preach the good news to all creation." All other things the Church does are simply means to this end. Perhaps but there are over a billion Christians in the world and I don't think it's possible to deduce the motivation of all of them from a single passage in the bible.