I don't know how much bias the fine structure constant has on the function of cognition, but I think we can all agree that constats incompatible with higher level biological function like cognition would never produce arguments in favor of their typicality.

The answer is: A lot. When looking at fusion processes that create carbon, if the strength of the electric force (quantifiable as the fine structure constant) were just 4% different, our universe would never have produced enough carbon to create life as we know it. The limit is even tighter for the strong nuclear force - less than one percent. If you pick arbitrary constants, you'd very likely just end up in a universe that contains only protons and no higher elements. And it gets even weirder when you start looking at gravity, because most universes should actually have collapsed again long ago or expanded so fast that no elements could form. Some of these fine tuning problems can even be looked at in the absence of intelligent life, because even for a liveable universe they seem ridiculously fine tuned to support what we actually see in the sky.

I carefully chose my word "function" instead of "existence".

Give me two different universes where cognition exists but where the fundamental constants differ. Would you expect the ability to perform syllogism would be fundamentally biased to reflect the constants which brought about their existence?

Easy. I present you two universes, one with our cosmological constant and one with a slightly smaller but still nonzero one. The differences would only become apparent over distances greater than a few billion light years or so. Out planet, solar system or even the entire galaxy would be virtually indistinguishable. But inhabitants of both would wonder how the cosmological constant got cancelled out so precisely against the QFT vacuum over so many orders of magnitude when studying the sky. No bias required.

Yes it's called the Anthropic principle