The series overall (by which I mean, the PS2 trilogy of 4, 5, and 0, which were the smash hits of the franchise) is Gundam by way of Topgun. The story is melodramatic and thematic, rather than grounded or analytical. You can either buy into it or laugh at it, and get the same amount of enjoyment either way.
That said, the story for 7 is a bit of a mess. The cutscenes have a rather severe case of separation from the story of the gameplay, since the story of the cutscenes focuses on a cast of side characters who only occasionally have a role in the story told through the missions. And I feel that the emotional buy-in of the player is going to be focused on the cast used during the missions due to that being what the player is actually playing through and investing in.