So everyone seems to agree that recurring round keys in a Feistel network (eg. using the same key for every round) are a massive security leak. When researching this, the only thing I found is the Slide Attack (https://en.wikipedia.org/wiki/Slide_attack), in which a slid pair is found, which can be used as a plaintext-ciphertext pair of the PRF used in the network (which is the same / repeated in the network).
My problem with using this attack to prove that key reuse is insecure, is that this only works if the PRF is vulnerable to known-plaintext attacks, ie. the key / part of the key can be recovered if a plaintext-ciphertext pair is known. Now, my understanding is that if one was to just use a keyed PRF which does not leak parts of the key from a cipher-/plaintext pair, the whole network would be secure, which I am relatively sure is not the case.
In addition, what I do not get is why a Slide attack completely breaks the algorithm; according to all sources I have found, one still has to find $2^{n/4}$ cipher-/plaintext pairs, which of course is significantly less than the original $2^n$, but still not polynomial, ie. I can just quadruple the block size to get the same amount of security.
What information am I missing that invalidates my claims, so that cyclic keys really make a Feistel network insecure?
