My understanding is that protein and DNA helices show the handedness that they do due largely to the [intrinsic chirality of their components][1]. Note that in [natural biomolecules L-amino acids and D-nucleic acids predominate](https://pubmed.ncbi.nlm.nih.gov/1802647/). This apparently leads to a subsequent bias in their respective polymers.

I believe that it has been demonstrated that [artificial alpha helices constructed of achiral amino acids demonstrate inversions between left and right handed forms](https://www.asiaresearchnews.com/content/researchers-fix-chirality-helical-proteins)- these then need to be stapled with extra molecular bridges to hold left or right handed orientation.

Thus, I don't think that there is a right-to-right or left-to-left association. **In all cases, I think it's just that the biased handedness is baked into the structure of natural amino acids.**

  [1]: https://pubmed.ncbi.nlm.nih.gov/32969653/