Gravity, dark energy, dark matter or the arrow of time in no way conflict with QM.
There isn't yet any successful quantum theory of gravity, but it's universally believed in the physics community that there will eventually be a quantum description of gravity. Dark energy and dark matter are merely components of the universe whose precise character is not yet known, but again, everyone believes that whatever they are, they will be described quantum mechanically. The arrow of time is merely a consequence of entropy being low in the early Universe.
The reason why physicists universally believe that the Universe is quantum mechanical is that it's impossible for QM to describe only a part of physics. If one aspect of physics is quantum mechanical, it "infects" every other aspect of physics and forces it to be quantum mechanical. You can't have elections obey quantum mechanical laws, but the gravity they produce be classical. It's really all or nothing.
I don't see why that has to be the case other than mathematically it looks like QM "infects" everything as the theory stands now. But nature doesn't have to play along. Also, I forgot about spacetime. Is it quantum mechanical, relativistic or something else? And saying the universe began at al low entropy doesn't explain why it started out in that state.
You cannot construct a logical theory of physics in which some aspects of physics are quantum and others aren't. That's what I mean by Quantum Mechanics infecting the rest of physics.
This is why after the discovery of Quantum Mechanics, there was a drive to formulate quantum versions of all fundamental theories.
Nature does have to play along, because whatever the correct theory of physics, it has to be logically coherent.
Either everything is quantum, or nothing is. Given that we are pretty darn sure that most of physics is quantum, we're pretty sure the answer is that everything is quantum, not that nothing is quantum.
There are different ways of formulating quantum theories of gravity (in fact, you can derive the Einstein equations fairly straightforwardly by trying to formulate a quantum theory of a massless spin-2 boson). We don't know which of those theories is correct yet, but it's not as if there's no way to quantize gravity.
There isn't yet any successful quantum theory of gravity, but it's universally believed in the physics community that there will eventually be a quantum description of gravity. Dark energy and dark matter are merely components of the universe whose precise character is not yet known, but again, everyone believes that whatever they are, they will be described quantum mechanically. The arrow of time is merely a consequence of entropy being low in the early Universe.
The reason why physicists universally believe that the Universe is quantum mechanical is that it's impossible for QM to describe only a part of physics. If one aspect of physics is quantum mechanical, it "infects" every other aspect of physics and forces it to be quantum mechanical. You can't have elections obey quantum mechanical laws, but the gravity they produce be classical. It's really all or nothing.