"Furry" and "fury" is actually a pretty bad example of this rule because of what "r" does to vowels, and "u" in particular.
In any case, historically, a double consonant meant the consonant was long, which often meant the vowel was shorter to compensate. As English evolved, it lost phonemic consonant length, and compensated by latching on to the vowel length instead, hence the modern rule: doubled consonant means short vowel (ignore the Great Vowel Shift for the purposes of this discussion). The writers of English noticed this pattern and started applying it to (some) cases it never applied before, hence the doubling rule for inflections, to help distinguish from clipped silent E's.
As for "why ck", most words with a final /k/ are spelled with "c", and need the "k" when inflected to prevent the "c" from "softening" in front of the "e" or "i" in the ending. Also, it just looks nicer than "kk", and we have the option, so why not?
By the way, the double consonant rule is also where the "d" in "judge" comes from (and why I will never pronounce "kludge" with a long U, don't @ me): Because of the silent E, the "u" would be long, so the "g" must be doubled. But the "g" is also softened by the silent E, which means it's pronounced /dʒ/, so "gg" would suggest the wrong sound, but "dg" wouldn't.