Though SO and Programmers are obviously two different subjects, someone who is an expert in one should also be an expert in the other. So why are their reputations kept separate? Similarly, though I don't participate too much in superuser.com, but at least my SO rights should help me have the same rights on superuser, no?
The direct answer to your title question is what Yannis said: If you don't participate on site X, you don't know enough about it to have all of the same privileges as you do on your favorite site. An especially common problem is people from site X misunderstanding the scope of site Y and voting to migrate things which Yers would instantly recognize as off-topic. There's a reason we have a chatbot to warn us about any SO comments that mention Programmers ("this is subjective, so it should be on PSE" is a surprisingly common comment on bad SO questions).
However, there is a toned-down version of what you're asking for in the form of the association bonus. If you have at least 200 reputation on any Stack Exchange site, then you automatically get a bonus 100 reputation on every new Stack Exchange site that you join. So once you reach 200 rep somewhere, you essentially gain the power to comment and upvote everywhere, but if you want to downvote, close vote or delete vote you still have to earn it. In my opinion this is a very reasonable compromise.
Also, there is a combined network reputation, but as far as I know it's only used by the chat system, so it doesn't really matter for your question.
Knowing how to implement code may be different than being able to architect or design it.
In some sense, it's like saying, "why aren't construction workers able to be architects?"
Some construction workers could probably do better architecture work than most architects. Some architects probably could do better construction than most construction workers.
But just because someone is a construction worker doesn't mean they can design an efficient house (even if they can build it) and vice versa. Both jobs have different skills required.
It is true that they might often overlap, but it is not guaranteed.