Because it's a lot easier to balance if classes buff themselves, rather than having one dedicated class to do it (plus, you don't have to burn a party slot on a buffer). It's much easier to tune on a job-by-job basis, to keep every DD on an even keel, and doesn't require accounting for a huge variety of outside buffs that have to be accounted for (e.g. difference between no BRD, one BRD, two BRDS, BRD+COR, and whatever songs/rolls might be selected (which might well not benefit all jobs equally, requiring some compromise or one or more jobs getting suboptimal buffs)).
And, if I'm honest, when I think about job roles, I really only care about activities done at the level cap. Could be small man, could be large groups, but I frankly don't give two craps about XP party. That said, if there's one job every single party is better off with at every single level, it's BRD. If that's not poor game design, I don't know what is.
Plus, how can it be a terrible breakdown, as those are the 3 major archetypes for any MMO. Buffer would be #4, but can easily be incorporated into the first 3. For FFXI in particular, BRD almost becomes a 5th, because it is so incredibly valuable compared to any other class, in any situation. Every other job can be replaced with very similar end result, except for BRD.
Quote from an old LS mate: "Asuran Fists' modifiers are 50% Acc, 50% BRD".