As much as I enjoy playing other races (and unlike others, I think DAI did a good job of actually making me feel like playing an elf), I understand they are a ****** to program.
Aliens from vastly different societies with very different morals would be difficult to implement, not just because of different body models. Ideally, they would have to write entirely different dialogue for a lot of conversations. Done right, a Salarian would have a different speech pattern even. Imagine all the extra voice acting. Unless the VA was insanely talented and versatile, you'd probably have to hire more than the 4 voice actors that DAI had, and that was quite a lot of work already.
The biggest issue I had with the inquisitor was how bland s/he was. I don't want this repeated in ME:A, but the "pathfinder" already sounds like a space inquisitor. So I'm prepared to find everyone infinitely more interesting than my own PC...
I'm sure part of the blandness was the mixed feedback to Hawke. But some of it probably was just avoiding having to write and record even more dialogue.
I vastly prefer a human PC with a charismatic personality like Shepard to different-looking versions of boring sameness.
Now, if ME:A had a Turian, or even better, a Quarian, as a set protagonist, I'd be all over THAT.
Before Andromeda was announced, I kept envisioning a personalized small-stakes story of a space adventurer or outcast, preferably an alien, maybe even from a new race. Not THAT much unlike what we have now, but in the Milky Way. And not another evil race threatening all life storyline (seriously, Bioware?!). I wanted a game where you are maybe looking for a family member gone missing. And during your desperate search you meet all kinds of people, maybe run into some serious social issues, maybe more race conflicts. A game set directly after the reaper war, or a few decades later, would offer plenty of tragic stories and tension over resources. It could have been something akin to Fallout in space, the Milky Way as a wasteland. I like games that focus on the psychology of extraordinary circumstances. ME:A could do that too but I kind of doubt it.
I don't need an omg-how-epic-badass story each time. Which is why I liked DA2 quite a bit. It was a more personal story. I'd like something like that for Mass Effect. But instead of staying in one city, I want to travel all over the galaxy in search of whatever.