The general idea behind Macross 7 sounds promising. About 40 years after the events of the original series, a colonization fleet sets out from Earth on its way to the galactic core. This is the 7th of the Macross-class colonization ships (thus the series name), a huge ship capable of carrying a million colonists. That leaves plenty of opportunity for both military and civilian story-lines, and lots of options for both internal and external conflict. An opportunity that unfortunately is missed.
It seems the writers took a look at the original Macross series, saw "alien threat that the military can't handle being neutralized by a civilian singer", and decided to hit the viewer over the head with that premise. As far as I'm concerned, that was a minor plot device in the original Macross series. The real appeal of that original series lay in humanity dealing with alien contact (at the macro level) and the "dream girl vs the girl right in front of you" relationship struggles of Hikaru (at the personal level). Macross 7 takes the "singing vs aliens" part and elevates it from a minor component to the entire premise for the series.
To make things worse, the central characters that the show's writers chose to build the story around are just awful. One: Basara, a socially isolated musician, who just happens to also be an amazing hoverbike rider/street fighter/fighter pilot, who constantly interferes in military matters and runs out on his friends. Two: Mylene, the spoiled teenage daughter of the military and civilian leaders of the fleet, constantly complaining about her protective bodyguards, being shopped around to older men by her mother for an arranged marriage.
The way this series theme is executed is awful as well. From the very first episode, Basara jumps into an unauthorized Valkyrie fighter (controlled by a guitar, for some reason) and flies out into the middle of battle, and proceeds to sing at the enemy. This appears to upset everyone on his side, from his band-mates to the military, though it causes only mild confusion to the enemy. And he does it repeatedly, episode after episode, for no obvious reason except possibly that he's an idiot.
The one moderately decent aspect of Macross 7 is that some of the music is fairly decent, as far as synth-pop-rock goes. But like almost all music used in television shows, the same songs are re-used so often that you'll be heartily sick of hearing them. Even watching only the first few episodes, I went from "hey, that Planet Dance tune is decent" to "oh, please, not Planet Dance again." Repetition takes the music from "moderately decent" to "painful to hear."
The fact that Macross 7 generated several years worth of an anime series, films, and OVAs means that someone must have liked it. I can't say I understand why.