I love Awakening but the existence of the MU, from a story perspective, really bugs me.
I know it's supposed to be "you" in the game, but somehow I can't overlook the fact the MU obviously isn't me, so I try to think of it as a standalone character, and when I created my MUs I took this into account. So I would create an MU with a name I devised and think of it as just another character with his own backstory.
But then I started seeing people online who sort of put themselves in MU's shoes, even going as far as marrying their favorite opposite gender characters, which is something I didn't consider when playing for the first time. For example, my favorite girl is Cordelia, but I didn't want her to marry MU in my current file because I thought there were male characters who were better for her, like Lon'qu and Stahl, and my choice fell on Stahl since he's among my favorite males and they work very well together (also their supports are cute). But in the end, I did feel somewhat bad about not marrying her (especially after seeing her supports with MU), and I wanted to make MU marry another girl I liked, such as Miriel or Cherche.
Anyway, even though the MU is supposed to be a self-insert, truth is they have a character of some sort and I think the writers didn't succeed in making him/her as generic as possible so you could really fantasize about being in MU's shoes, or they could've included different writings based on personalities... I don't know. Whenever you're given the option of creating a character like this, I can't help but not feel like I am the character. In Pokémon, for example, I tend to use canon names, because there's no way I'd see myself as the protagonist (and in Pokémon he's silent which means the immersion is bigger).
I welcome the gameplay value of MU, though. Fully customizable units FTW.