Infinity is a fact of life; hard to experiment with in a lab, or even on a digital computer, I agree, but that doesn't mean it's not real. Intelligence is, after all, also something that only exists in your mind. Like mathematics, it doesn't need to conform to common sense Newtonian physical rules, any more than quantum phenomena do. Neuroscience shows that what you see as "reality" is actually a model constructed in your mind using sensory input extended by calculations of probability and a lot of estimation - very like mathematics. That's good enough to keep you fed & breathing, usually, which is what it was designed for. External reality looks very different to creatures with different senses - who's to say who's right? The concept of infinity does often come into play when linear reductionist logic reaches its limits and that is indeed when an apparently satisfactory theory sometimes fails.

"Too stupid to breed" is the kind of thing eugenicists (and racists) say in private, using polite circumlocutions in public. We need to bring that thinking out into the light of day to deal with it.