Construction of a "simple", nothing-up-my-sleeves, provably KPA resistant symmetric cipher Why is AES secure? Apparently there is no answer - Why is AES resistant to known-plaintext attacks?.
With this in mind, one would obviously want a cipher that is mathematically provable to be resistant to KPA. How would one go about constructing such a cipher? Has it been done? Can it be done? Is someone doing it? Why hasn't it been done? Can you blame mathematics atleast?
When I look at AES, I see a bunch of random up-the-sleeves operations, with, as aforementioned, mostly no explanation. Why can't there be a simple, efficient and secure algorithm to encrypt things?
Imagine a simple (e.g. xor) cipher with a 256-bit key that is applied to each 256 bit aligned block of the plaintext. Suppose it wasn't vulnerable to KPA and other attacks. Then it would be equally secure as AES-256, if not better, given the potential flaws of AES. Problem solved? Unfortunately not; contradiction.
With this in mind, one would obviously want a cipher that is mathematically provable to be resistant to KPA.

Any scheme that has a message space larger than the key space and is unconditionally provably resistant against known-plaintext attacks while being efficiently computable immediately implies $P\neq NP$. As we don't know for sure whether $P\neq NP$ holds and this having been a famously tricky question to answer it seems like it is really hard to build such a cipher.
However if you're willing to make assumptions, we know provably secure constructions. The issue with that is though that most of these assumptions and constructions lead to ciphers that offer no real security advantage over a heuristically well-designed cipher like AES while being much much slower.

When I look at AES, I see a bunch of random up-the-sleeves operations, with, as aforementioned, mostly no explanation.

While this may look to be the case at first glance, the design of AES was very considerate. If you wish to learn more about this topic I suggest you read the book on why AES looks the way it does: &quot;The Design of Rijndael&quot; by Rijndael and Daemen.