You're right that a radix doesn't scramble the key, but the quote you've picked is a qualified subset of hash functions. That paragraph is attempting to define a practical/good hash function that is used in specific ways. Not all hash functions scramble the bits, and the Wikipedia article is very clear about this if you read the whole thing.
You skipped over two important sentences that came before it, and a whole sub-section on radix hashes after it:
"A hash function is any function that can be used to map data of arbitrary size to fixed-size values." (very first sentence, emphasis mine.)
"In some cases, the key is the datum itself." (Right before the 'scramble' quote)
String hashing is sometimes similar to radix as well: "Simplistic hash functions may add the first and last n characters of a string along with the length" and I've seen string hashes in production that do only the first n characters and stop. That kind of hashing is frequently useful in small, embedded systems, video games, etc. where you have a limited set of strings and a good idea of how well distributed the keys are.