Your theory makes sense in an evolutionary context. It is possible that all cells and organisms have some general intelligence. Humans do not have the ability to recognize this because evolutionarily it was only helpful to recognize intelligence when it could pose a threat to us. And the biggest threat to us in general was other humans as we are tribal animals. So we don't see it, we only see specialized intelligence that historically posed a threat to us.

It would explain why most "experts" didn't see GTP-4's abilities coming. Many of them expected that it would take a major algorithm or technology improvement to do "real intelligent" things, because they fundamentally misunderstood intelligence.