Why is the security of block cipher not a function of key and tweak?
Generally speaking, in proofs of security for Feistel ciphers with various numbers of randomly selected round functions, the secret 'key' is the set of round functions.  Thus, when Patarin or whoever gives upper bounds on the Adversarial advantage for distinguishing a Feistel cipher with $k$ rounds from a random permutation, the key 'length' (i.e. the size of the key space) is implicit in $k$, the number of rounds.  Keep in mind that many of the bounds (e.g. of Patarin) are information theoretic, so brute force isn't really an option -- that is, even someone with an infinitely powerful computer would not be able to distinguish the Feistel cipher from a random permutation better than the relevant bound.

Tweaks are not commonly included mostly because tweakable block ciphers are a recent innovation.