In addition, some achievements can be very tough for some characters, given their spec. For example, "Wrecking ball" is not realistic for a level-capped healer to obtain. I would like to have the achievement/points, but I'm not about to fully PvP gear a Ret spec in order to get it.
Anyway, I hope Blizzard decides to go all in on the account-wide achievements. This is the first time in five years that I've felt strongly enough about a topic to make an appeal on the forums.