Let's not forget that competitively Ice, one of Dragon's previously-only-two weaknesses was one of the worst defensive types due to the commonplace Flamethrowers, Close Combat, and Fire Blasts. Fairy only having to worry about Poison and Steel, the least used offensive types, is pretty handy if you ask me.
It's even more worse when consider that Ice's only major use competitively was being used as a coverage move, notably through non-Ice Pokemon that learn Ice Beam and such, mainly Water-types. Having Fairy being weak to the least used offensive types means they can stand up to Dragons better plus quite a good amount of Fairy-types have some variety in their moves, notable ones being Togekiss, Clefable and Slurpuff due to their versatile movepools.