The problem with shmups and stories is that there is a clear contradiction
A) The invading army has completely defeated your planet/country military forces.
B) You can defeat the invading army all by yourself.
Metroid has a great story for a game with shooting, because you are a superhuman with a super armour, killing alien bugs and animals who are very inferior to you, it is almost like an alien safari, and only the bosses are more equal to you.
But in Shmups you beat all by yourself a whole alien army that has technology more advanced than that of your planet. And you must be a godlike being, since all your compatriots were utterly defeated and you are beating the invading army alone.
If I had to make a shmup with a story the enemies would be non intelligent alien parasites that float in space, or a game in the future in which you travel inside a human body shooting bacteria and viruses as a form of future medicine.
