Out of interest is there a simple proof that you couldn't make an achiral protein-building system? Is there a level of complexity of carbon chemistry at which chirality is unavoidable and below which there's an insufficient range of possible structures?
Sort of, and yes. A chiral molecule is any molecule with four non-identical sub-groups bonded to one Carbon atom. (There are also lots of other sources of chirality, but that one will do to start with). So, almost any complex carbon-based molecule will have a non-identical mirror-imaged form.
The more interesting question is whether mirror-life is likely to have evolved elsewhere in the universe. Life based on much the same building blocks as ours, but all components the mirror image of ours. Classical chemistry provides no reason why not. Quantum physics reveals that the weak nuclear force is itself chiral, and that there's a tiny difference in stability between Earthlife amino acids and their mirror-world alternatives. It's only about one part in 10^24, but there's a tipping-point in that L bonds stably with L, D bonds stably with D, and mixxed amino-acid polymers are much less stable than pure-L or pure-D ones. Ours is the mort stable. Evolutionary coin-toss, or inevitability?.
All speculation until we find some other instances of life. May be a long wait.