"Not allowed" by whom? Industry practice? At this point with the modern distracted, over-stimulated consumer, I would assume that these sorts of gentlemen's agreements are headed out the window

Also there are multiple examples of production companies owning their distributors which predate Netflix - think Disney and Buena Vista

Not allowed by the Supreme Court. https://en.m.wikipedia.org/wiki/Studio_system

That's an incorrect conclusion you're drawing. That ruling doesn't apply an inherent legal barrier to Amazon's situation with Landmark at all. It does not ban movie production companies from owning distribution. An anti-trust review for a given context would be required to determine whether a combination is in violation of anti-trust laws. The Supreme Court in the Paramount case found that particular scheme was in violation, that is all.

This also had the key component of studios holding exclusivity rights and only showing movies in their theaters.

Isn't that what Netflix/Amazon Prime Video are doing? Aren't they owning the distribution of their in-house produced shows?