Andromeda would have been the prefect game to do that. Dragon Age 1 style where you choose your race (and therefore Ark) and play a race-specific intro before you go out into the brand new Galaxy.
Like I kind of get the desire to play other races, but at the same time I don't when specifically thinking about ME. A central facet of the ME franchise is the human experience of discovering a galaxy outside of ourselves and the limited view that we have, both literally in our real lives and within the game's setting as well. Andromeda is a major change in setting in large part to maintain that ability to discover something new and alien. Which I don't think was really necessary, as there was plenty of mystery in the Milky Way especially after ME3's ending, but here we are. Making it so we could be multiple races would drastically change the tone and feel of the series.
It's something I enjoy about DA and other fantasy cRPGs, but it definitely affects the story and interactions because they have to make it fit each race and only at certain moments do they really make your background important and even then it's normally just a superficial nod and not a serious factor in the way the game plays out.
Despite the many times I've played DA games and all the Origins I still prefer the ME setup as it provides a more tailored experience. It's one of the things I actually liked a lot about DA2, despite its many issues.
That said I wouldn't mind at all spin off games that focused on an alien race as the playable character. There is certainly a lot to explore.
One too many in my opinion.
There will always be two other humans for romance options. One Male and one Female.