Why does the universe need quantum superposition?
Because of the wave nature of matter. Check out the Wikipedia quantum supposition article:
"Quantum superposition is a fundamental principle of quantum mechanics. It states that, much like waves in classical physics, any two (or more) quantum states can be added together ("superposed") and the result will be another valid quantum state; and conversely, that every quantum state can be represented as a sum of two or more other distinct states. Mathematically, it refers to a property of solutions to the Schrödinger equation; since the Schrödinger equation is linear, any linear combination of solutions will also be a solution".
Note that the Schrödinger equation is a wave equation. We can diffract electrons because of the wave nature of matter. And neutrons too. And protons. Check out Direct Measurement of the Quantum Wavefunction by Jeff Lundeen and others. He reckons wavefunction is something real that can be measured in the lab.
My question is not about the nature or reality of quantum superposition, superposition is a fact and no argue about that. My question is: What is the purpose of superposition and why does the universe need it?
It doesn't need it per se. And it doesn't have a purpose per se. That's just how the world is. Everything is fields and waves. That's what quantum physics is all about. These waves can "ride over each other" or intersect or combine, whereupon they're in superposition.
Every law of physics has its necessity, and makes perfect sense that the universe cannot work without it. But when thinking about superposition, it seems physics laws will work fine with or without superposition!
These laws don't have any real existence in their own right. We observe things and take note of evidence, then we come up with theories that include "laws" that describe how the universe works.
Edit: I am not questioning superposition itself, but the wisdom behind it. Imagine a world without superposition
I'm afraid I can't. Because I can't imagine a world without waves. A world without waves isn't much of a world at all.
where every state is determined from initial conditions, what will change in the universe?
I can't say that I know for sure. But I fear the answer is nothing. A world without waves isn't much of a world at all, and nor is a world without change.