Like others have said, it would be cool to see quadsort stacked up to other current state-of-the-art sorting algorithms.
When sorting single words consisting only of the letters A-Z, for example, you can think of it as the same thing but with 26 buckets (27 if you pad with spaces instead of As) instead of 10. Or you can think of it as a specific subset of numbers in base 36, if that makes more sense to you.
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.