I don't feel like it's fair to disregard the loyalty missions when they comprise the bulk of the story. As a comparison, consider an episodic television series. There might be a thin story thread linking a season together, but for the most part, each episode features its own little adventure.
I think there are a few distinct differences between a t.v. series and Mass Effect to make this comparison a little weak.
For starters, most television series are designed to be open ended because the creators are hoping to get multiple seasons from their concept. By its nature, the narrative of the show is going to be weak because they want to leave it as flexible as possible so they can adjust to the network's time frames. However, this doesn't preclude them from having to worry about the narrative either. Many times shows are created with either a specific character story to tie the whole series together or an overall conflict that can be addressed from time to time.
Take The Mentalist for example. The larger narrative is the conflict between Jane and Red John and his determination to hunt down the man responsible for his wife's murder. Most of the day to day stories, however, are just the police force solving your average homicide. Even though much of the series' stories are unrelated to the narrative doesn't preclude us from being able to judge the ones that deal with Red John and how they're pretty ridiculous whenever they come up.
And this brings us back to Mass Effect. It wasn't developed like a t.v. series and had a very distinct beginning, middle and end planned out. Now, you don't need an omnipresent narrative for the structure they adopted to work but you still need those narrative "episodes" to be good and for those story "episodes" to feed back into that narrative.
And they weren't and they didn't. There's no excuse for that since the developers knew the exact structure they were working these side quests into. They don't have an excuse like the network yanked their show a year before they thought and had to rush all their narrative heavy plot into the final episode in order to conclude it. The entire motivation for ME2 was assembling a crew for this suicide mission but no real effort was made to work with the whys and the mission itself - which was meant to be this great coming together of all the stray elements - was so bland and generic that pinning the entire narrative on it made it come falling apart when it flopped.
Not to mention the story of ME2 didn't help the overall narrative of the entire franchise. There are some basic structures you'll often notice in trilogies and ME2 didn't hit any of them. It really felt like a spin-off jammed into the middle of its original plot with the hope the audience wouldn't notice. Probably the most egregious stumble is the fact that the final decision in the second has effectively no impact on the third.