Because Blizzard is trying to diversify their endgame, and having these bonuses be exclusive to raiding is weird when they're pushing for things like M+ to be an endgame in their own right.
Azerite armor is basically tier sets writ large; you can have raid pieces with raid-friendly traits, WQ pieces with WQ-friendly traits, PvP pieces with PvP traits, so on and so forth.
That said, dropping the class-themed aesthetic is due to saving resources and little else. I don't buy the excuse that they went through all the possible class fantasy permutations or couldn't come up with an Old God theme Paladin set or whatever. Hopefully it means we get more/better armor sets from other activities now that they need to design 4 sets/raid instead of 12, rather than have raid armor be head and shoulders above everything else in quality.