Your post is a good example for why cascades are so dangerous.
hash1(hash2(...)) is not as secure as the stronger of the hash functions, it may only be as secure as the weaker of the hash functions. Your example is sha1(md5(...)). Well, md5 is no longer considered collision-resistant, which means that sha1(md5(...)) also isn't collision-resistant. If you're able to obtain two different inputs that are mapped to the same hash by md5, computing the sha1 of that hash is still going to lead to the same value, i.e. a collision overall.
So your assumption that an attacker must defeat both is clearly wrong and dangerous. In the case of hash functions, I believe it would be safe two concatenate the hashes (instead of composing the functions), but now you have a bigger hash size in addition to a slower running time.
hash1(hash2(...)) is not as secure as the stronger of the hash functions, it may only be as secure as the weaker of the hash functions. Your example is sha1(md5(...)). Well, md5 is no longer considered collision-resistant, which means that sha1(md5(...)) also isn't collision-resistant. If you're able to obtain two different inputs that are mapped to the same hash by md5, computing the sha1 of that hash is still going to lead to the same value, i.e. a collision overall.
So your assumption that an attacker must defeat both is clearly wrong and dangerous. In the case of hash functions, I believe it would be safe two concatenate the hashes (instead of composing the functions), but now you have a bigger hash size in addition to a slower running time.