Why not? Enough games have happy ends, why not have one that's mostly grim but still has one ending where the hero can live? Also it's not stated that the galaxy writes him off as dead, it can work both ways, it depends on the player's imagination. If your Shepard lives and will be found, everyone will know 
I know it's a small consolation for those who wanted to see more, but still.
Why not? Because the game's story is supposed to be shaped by player choice. If the player wants to have a "rainbows farting unicorns" ending (or whatever the hipsters are calling it these days), and they've been playing a game to reflect that, perfect SM and all, why shouldn't they get it? Isn't that what "player agency is all about? Shaping your own story rather than watching one on the screen?
If I wanted that, that's what tv is for.
As for Shepard being written off, the crew's holding a funeral for him/her. They made a plaque for the memorial wall and anything. It's only because the LI is sudden;y Force-sensitive that it gets interrupted. It's not like Hackett's voice suddenly comes over the intercom saying "we found Shepard. He/She's alive!"