Among philosophy academics, it’s somewhat popular to reject the Copenhagen Interpretation of quantum physics – the one we all have an ambient familiarity about that says that the universe is random

It doesn't, though. The Copenhagen interpretation is not the strong claim that the universe is random, nor is it the strong claim that the universe is predeterministic. Bohr rejected an axiom called that of statistical independence, arguing that in reality it is physically impossible to separate yourself from what you are trying to measure, as you are yourself a physical system that acts on the system through trying to observe it and it acts back on you. He believed this inability to separate yourself from the system creates a limitation in the maximal amount of human knowledge one can gain about a system as gaining knowledge about some parts of a system inherently disturbs and thus erases knowledge about another part, a principle he called the principle of complementarity.

Bohr thus saw quantum mechanics as kind of a "final theory" at the limitations of what is possible for humanity to know about nature, rather than as a direct description of nature as it really is. He once stated that "physics is not about nature, but what we can say about nature." It wasn't meant as a strong claim about the underlying ontology of the universe, but instead a position that the underlying ontology is fundamentally unknowable due to the principle of complementarity. Heisenberg agreed due to his uncertainty principle. He did not outright dismiss the possibility that there are hidden variables, but said that even if they exist, the uncertainty principle makes it impossible to measure them, so it is pointless to speculate on them.

The Copenhagen interpretation isn't the strong claim that the universe is random or not random, but instead the viewpoint that fundamental physical limitations prevent the construction of a measurement device that could actually prove nature in such a way to reveal how it actually is at a fundamental level, and so any speculation regarding that is unfalsifiable and there is no possibility to choose which is correct vs incorrect, so there is no point in such an endeavor. It does leave open the possibility of hidden variables, but does not leave open the possibility (if the interpretation is correct) that there are knowable hidden variables, if an underlying ontology exists, we can't know it. It's a claim about epistemic limitations rather than an ontological stance.

When it came to the US, this was largely during WW2 when the Manhattan project was going on. Americans were much more practically minded and not philosophical because they were trying to build something rapidly for a war effort. This led the Copenhagen interpretation to morph from an argument based on physics and philosophy as to why we cannot meaningfully know the universe's ontology to a purely utilitarian argument that we should "shut up and calculate" because metaphysics is "a waste of time."