I think you're confused about recommended symmetric vs. asymmetric encryption key lengths.
Symmetric ciphers, such as AES, can generally use any number for a key, so 256 bit AES gives you 2^256 possible keys. That's more than one key per every atom in the observable universe. Even with Moore's Law, it would probably take until the heat death of the universe to exhaustively search that key space. That's a plenty "realistic" key size.
In contrast, asymmetric encryption, also known as public-key encryption, such as RSA, can only use numbers that are the products of two large prime numbers. So that severely limits the number of useful keys within the key space. That's why public key encryption requires 4096-bit or larger key spaces today.
A 256 bit AES key is the equivalent of about a 15 kilobit RSA key.