This seems somewhat unlikely because of compatibility of chirality. Many molecules aren't the same as their mirror image (just like your right and left hands), and chirality is what distinguishes these molecules from their mirror image (a "right-handedness" or "left-handedness").

All life on Earth uses a set of compounds with the same chirality. Enzymes are built to catalyze reactions that exclusively produce the correct chirality of product. In fact, for some of these molecules, their mirror images are actually toxic.

In contrast, non-biological reactions generally don't have such a strict chirality preference. In general, you produce a mix of both "handednesses" in most reactions not involving something extremely selective like an enzyme.

So in abiogenesis conditions, the selection of our current chirality rather than a different one was likely due to chance. If it happened multiple times, it's unlikely that it would have given the same chirality every time.

As an aside, Dirac's statement is so interesting because 1) the angular momentum carried by such a field configuration is independent of the distance between the electric and magnetic charge, and 2) it only requires one point magnetic charge to work.

So as long as there is at least one magnetic monopole somewhere in the universe, his argument works.* What if there's genuinely only one? It's an interesting scenario to think about in terms of the limits of the scientific method; for example, if that one monopole passed through an experiment and left our Solar System, never to return, that experiment would essentially be non-repeatable and therefore non-verifiable.

*in a classical universe; not sure whether GR or QFT impact this statement.

The C=C=C=... structure doesn't seem to form, because polymerization usually results in single bonds between the monomer units. But we've observed something similar, namely, polyynes, with alternating single and triple bonds: ...-C≡C-C≡C-C≡C-....

Taking this to infinity, we end up with the hypothetical Linear Acetylenic Carbon (LAC), which has a decent Wikipedia article: https://en.m.wikipedia.org/wiki/Linear_acetylenic_carbon.

Take note, though, that any finite chain is going to have to be "capped" on the ends by something that probably isn't carbon (for example, a hydrogen atom on each end), because the carbon on the end has one remaining bond that has to attach to something. You might be able to bend the chain around into a ring to avoid this, but triple bonds are pretty rigid so this might not be possible.

That said, there's a much more well-known example of carbon-only compounds: buckyballs, made of 60 carbon atoms arranged in a truncated icosahedron.

Even ignoring the fundamental subjectivity of the question, your reasoning only works if all distributions relating attractiveness to some feature are "simple", having only one peak. If instead, for example, the distribution is bimodal, then the average is going to be in a region that almost nobody finds attractive.