While I would love to see a game with a smaller scale plot as the OP suggests, if we are going to the chosen one and last hope for the galaxy, at least make it so that we become the hero over the course of the game instead of having that role thrown on you in the first couple of hours of the game. Likewise, there shouldn't be a major threat right from the beginning, you should slowly uncover it as you play.
If we look at recent BW games, they've had a habit of making you the last hope from pretty early on - from ME having Shep as the only human spectre and the only person who can save humanity from Saren once you've spoken to the Council (even if the actual threat was bigger) [let alone what happens in the later games], to DA:O making you the last hope to stop the Darkspawn as early as Ostagar and of course DA:I giving you the glowy hand of power and a massive hole in the sky only you can stop in the prologue of all things - and while I enjoyed these stories, they all lack a degree of build up, development etc. They just throw you straight into the deep end and say "you're amazing, go save the world". For me at least, being the hero is a lot more satisfying if I've actually in some way earned it. If I've worked my way up to it. If I've discovered that my character is special, instead of just being told.
For an example of how I'd suggest it be done, well, we can stick to Bioware games actually: Baldur's Gate. By the end of the game, you discover that you are a demigod, and that you are the only person in a position to stop your half-brother (and fellow demigod) from conquering the region in which the game takes place and ultimately raising himself up as a full scale god. And yet, you don't know this until well into the game. The events of the end of the prologue hint that there's something special about you, but it's nothing more than hints, while the story for much of the game is pretty low key, with you following a trail of evidence through what appears to be some well organised bandits creating and then taking advantage of a shortage of good quality iron. Eventually though you start to uncover both the true goal of the people behind these bandits, and the truth about yourself. And finally, you go and save the day. By then end you are the big damn hero saving the day from the evil guy trying to become a god. But the game builds up to it so much better than much of Bioware's more recent work.
This kind of story actually fits what we know about ME:A pretty well, with the whole exploration of a new galaxy theme. At first, you think there's no big unified threat out there, and you're just investigating worlds find places for colonisation and so forth. You encounter small conflicts and isolated incidents. But as you start to uncover more clues across different worlds, a picture of something big out there which is a threat to us begins to emerge (these mysterious alien remnants likely). Likewise, the player doesn't begin as something special. We are one of many people sent out to explore Andromeda. But as a result of what we learn out there, we are the only person who is in a position to act, and thus we have to be the hero.