AES is not an ideal cipher, nor is it intended to be an ideal cipher. AES is meant to be a practical cipher that offers a strength close to the key size. That means it is computationally infeasible to find the key even if given the plaintext and the ciphertext. AES - when correctly used with a strong mode of operation - produces ciphertext is indistinguishable from random if the adversary can choose the plaintext input to the cipher themselves (IND-CPA).
The next question is why people think that AES is better than other ciphers with the same key size. Cryptographers generally don't really think that. There are other ciphers that may have better characteristics when it comes to protection against side channel attacks. Other ciphers have a larger % of rounds to spare when it comes to protection against certain attacks. Or they may have a larger block size, or they do not have a clear mathematical structure etc. etc.
AES has been studied a lot, and few attacks have come close to breaking AES. It is relatively fast compared with other block ciphers, and it has a serviceable key and block size. The algorithm is well understood, and there are many hardware implementations of AES, including newer x64 and ARM CPUs. So it is standardized, popular, well understood, but not necessarily the most secure cipher. It doesn't need to be, for most situations it is secure enough.
When you are talking about implementing an ideal cipher you seem to go over the key requirements of a one time pad. The one time pad requires a key the same size as the plaintext / ciphertext. Moreover, you won't be able to distinguish a good key from a bad key for a single block. But what happens if you have multiple blocks to compare? With each block a specific key becomes more likely. As such, it makes very little sense to try and create an ideal block cipher.
The ideal cipher is mainly a theoretical construction, useful in proofs. But beware that inserting an actual block cipher in place of an idealized block cipher may not result in a secure construction. For instance, a hash function could well be secure when constructed using an ideal cipher, while it could be vulnerable with AES-256 due to related key attacks.