And actually, for most of human history, I think that adding a new person was, on the whole, more likely to add resources, particularly in agricultural communities and in times of war. (Which is why we've only seen the reversal of this trend relatively recently)

Well, yes; Malthusian models would even predict this, since if another person didn't add resources, that reduces resources per capita (the denominator increased, the numerator didn't), and this could continue until resources per capita fall below subsistence, at which point every additional person must cause an additional death/failure-to-reproduce/etc. and the population has reached a steady state.

So every new additional person does allow new resources to be opened up or exploited - more marginal farmland farmed - but every new resource is (diminishing marginal returns, the best stuff is always used first) worse than the previous new resource...