Why would emergence imply anything about non-physicality and non-locality? Temperature is a another common example of an emergent phenomena. An individual atom doesn't really have a temperature, only a large group of them do. But you wouldn't say temperature is non-physical and non-local, would you?

I am not sure, but I think you might misunderstand what emergent means. Take chaotic systems, in the math sense. Chaos is a well defined property of, say, iterated dynamic systems.

A linear dynamic, say x_n+1=lambda x_n, or x_n+1=(1-x_n), is never chaotic. But if you multiply them, x_n+1=lambda x_n (1-x_n), it depends on lambda if the system is chaotic.

None of the components are chaotic. But for specific combinations, chaos emerges as an property.

In physics, the mass of mesons and the nucleon is emergent. It's completely different from the constituents' mass. Different from an atom, where its mass is very close to the mass of its nucleus and its electrons.