As an AST, I agree. However, I'd like to add that any time a WAR or melee DPS comes my way, I'm in trouble. Because of the way the map is arranged, I'm often repositioning myself so that my comrades don't break line-of-sight while also trying to break the line-of-sight of other casters. But if a particularly strong DPS (or WAR) comes at me and nobody is paying attention, I'm left with no other option than to use CDs and try to run away. This often means I'm running around in circles and, eventually, into the midst of the chaos because I'm trying my best to spam AoE heals to keep myself and the party alive.
...And things just sort of go downhill from there.
As a side-note, I don't have a problem with casters. I actually often ignore them, or just move behind a pillar/wall for a moment. The only one that can sort of bug me is MCH. So I wouldn't recommend sending a caster after an AST, unless they've figured out something that I haven't seen or experienced yet.