The main issue with AST - particularly - is that it's so heavily balanced around buffing other party member damage that it has its own damage balanced around being low. If you look at high end 8 person party damage, ASTs contribute a lot through their buffs on their party members, which makes their total damage (personal attacks + buffs to party) very good. They have a wider spread because of RNG and player skill, but the top damage an AST can output is on par with SCH (which also has a party buff) as the highest of the Healer Jobs.
...the problem, of course, comes when you're in content where you DON'T have strong party members to buff. Or no party members at all. In those situations, you have your low personal DPS, and sure you can buff it, but you're buffing...your low personal DPS to be slightly less low.
In order for AST to do more personal DPS, it would need to do less party buffing (have weaker buffs) OR alternatively, all Healers would have to have their damage boosted (not a terrible proposition) which would make encounter design require bosses to have more health/tighter Enrages (which...would be pretty terrible). Alternatively, they could do something like make AST buffs stronger when used on themselves to make up that gap (something people have proposed), which is not a terrible idea since it would still be better to use them on DPS and Tank party members in 8 mans, but make soloing stuff or doing MSQ solo fights on AST less trouble. All around probably the best solution.
Note that pretty much every Job is capable of doing everything in the game outside of some hyper crazy stuff (generally only Tanks and sometimes RDM can solo prior expansion boss fights or stuff like that), some are just harder and some easier than others. Like WAR is great in solo Deep Dungeons because it has strong defenses, good healing, and good enough damage, but they can and have been cleared with every Job.
In any case, here's hoping the coming 7.0 rework fixes AST up. I'm always against the "advice" of "swap to another Job and do it", personally.