In our more limited experience, certain levels of complexity mean unpredictable outcomes.
As for why-not-DNA, I think about it in terms of "If there were some way that was faster able to adapt organisms than DNA changes, wouldn't most organisms accumulate substantial functionality via that pathway over time?"
Is this true, given https://en.wikipedia.org/wiki/Uncertainty_principle ?
However it is not clear if quantum effects are relevant at a biomolecular scale. Some experts[1] suggest so but these ideas are considered fringe by the mainstream.
1. Sir Roger Penrose
However it seems to me the deterministic vs randomness debate is of the same order as the existence of god(s) : we will never be able to prove or disprove it and we aren't able to make useful predictions out of the information one way or the other so we might as well just agree to disagree and move on.