Could ANY cipher serve as the foundation for a public key cryptosystem?
Your reasoning is flawed. Producing a cipher text for a given key from plaintext without the key is no easier than the reverse for symmetric ciphers. 
Without the key k, producing ciphertext $Enc_k(x)$ is every bit as hard as $Dec_k(x)$ for many ciphers it is the same operation entirely (e.g anything in CTR mode). And even for common block ciphers there is great similarity between encrypt and decrypt. 

For a public key system I need some operation which can be done without the private key. AES etc. do not supply one. If you have the key both operations are easy, without the key they are darn near impossible.