You can definitely do dungeons at any level. Although you will still be getting a lot of EXP, it syncs level seamlessly. However, yeah, I know how you feel. It does feel lame, like you're not supposed to be actually playing the game or something, but it was a compromise implemented so that those that only wanted to do max level stuff wouldn't take so long to access it because you have to do the entire Main Scenario to do the serious stuff.