You be whoever you want.

Whether or not monk's white damage is good is irrelevant though. They are roughly putting out somewhere between 50-70% of the damage an equally buffed and geared DD of a different job is. If you increase the damage of the weapon skills to put monks within 10% of the pack, the white damage doesn't affect that change. Counters also do not really factor in, as they are not a reliable source of damage. Counter is a nice semi unique defensive feature to monk, but you can't counter TP moves or magic, you gain no TP from it, and the overall damage dealt from counters is negligible in an endgame scenario, even if you were to tank the entire fight. Exception being perhaps if the mob used hundred fists, but then WAR with retaliation and arke gear is still leagues ahead on dps resulting from that.

The main reasons monk was so prevalent in the times you are referencing are also no longer present. We're no longer using crit atmas in abyssea, more jobs than monk have ilvl weapons, there's more defensive gear available to DDs than blackbelt, twilight torque and dring, and we're not in need of a job to cover several NMs' gimmicks in the same instance. Other jobs often failed to bring anything of value to the fights aside from their damage, and that's just no longer the case.