I think that newborn babies aren't "meant" to sleep deeply for long periods. They just aren't. Their nervous systems aren't developed yet (they ahve to be born before they're truly ready, due to the narrowness of the human pelvis since we walk upright). The first 3 months are often called "teh fourth trimester," and there is a lot of nervous system maturing that happens during that time.
I think there's a lot of support for the theory that babies on their tummies don't rouse themselves as often or easily, and so tend to sleep deeper, to the point that they can stop breathing. There's also a lot of support for the fact that babies sleeping with (or near) adults will breathe along with the adult, keepign them from going too deep.
So yes, I do believe that tummy sleeping contributes to SIDS and that back sleeping helps prevent it (but obviously does not completely do so; almost nothing in life is 100% either way). And when cosleeping and nursing, even in a real bed, you're both generally on your side, or you tuck baby into your armpit, face up.
I also think that "in the wild" our ancestors probably did not put their babies flat on their stomachs very often, if ever. If you don't have a modern (or even premodern) mattress bed, where exactly would you do that? Where would be safe and clean? Imagine putting your newborn face-down on a heap of skins, or a pile of straw or grass or wool. How does a baby tummy-sleep in a sling? In a hammock? On a cradleboard?
So yes, I think that putting a baby under 3-4 months to sleep on its tummy is probably not biologically appropriate for child development as we now understand it. Sure, it makes the child sleep more deeply. But newborns sleeping very long stretches undisturbed is *also* not really appropriate for child development as we now understand it.