I could ask the same about humans, as I had several people say they wouldn't play the next game if it had a mandatory elven protagonist.
What ultimately matters is one or both of aesthetics and cultural background. Some people find some races more appealing in those areas than others.
I'm not one of the people who said they wouldn't play with an elf-only protagonist, but I'll answer anyway. I don't expect this to apply to anyone except me 
I generally play partial-self-inserts (more morality and decision making, less appearance and name) to begin with, and depending on how much I replay a game and other factors, I'll do it again as something different. So playing as humans fits there, naturally, since I'm human.
Of course, since these games are so long, I don't always get to the point of doing anything significantly different, and sometimes I don't even want to enough, and I can enjoy replaying the same character just as I can enjoy rereading a book or rewatching a movie. The most significant deviation I've done is probably romancing Cullen on a subsequent playthrough, since my canon is a forever-alone lesbian (actually, most of my canons are. Heh
Heh heh
). And yet, I still romanced him as a human, partly because I didn't feel the need not to, and partly because I was borrowing my girlfriend's character anyway, so I had to.
Aesthetics do also play a role here, if I'm honest. While I could rail about the model-looks of Bioware's human female protagonists extensively, I'm not a huge fan of the elves, dwarves*, or qunari either, for quite different reasons. My body-type doesn't overly resemble any of them anyway, so, eh. Some people really like the faces of elves, dwarves, or qunari, but I think the humans look just fine.
*I actually like the look of female dwarves in DA:O/DA2, but I can't bring myself to play one in DA:I because of the effective retcon of how they look (since there is only one body type for everyone). In DA:O/DA2, they were still stocky and well-built; only slightly thinner than males. In DA:I they creep me out because they look like children with boobs
Also, I can't romance Cullen with them 
So long story short, I don't have anything against playing other races, I just default to humans. I feel like the people who have such strong opinions that one race or other is better to play as are very silly. We all have our reasons for liking different things. I would, however, be more interested in playing non-humans if they were more... well, non-human, as I say below.
My point was neither is there "anything too alien" in the culture of the elves and dwarves. They might as well be humans.
I think it would be very interesting to be able to play as a spirit in DA or Geth in ME (or other AI). However, I think they would be very difficult to write as a roleplaying protagonists - much harder than simply writing them as a set character. And it would be challenging simply because they are among the most alien characters in these settings, so naturally hard for humans to write.
This is also a factor for me, albeit in the opposite direction from elves
. There's an extra reason I like to play dwarves, even beyond my fascination with the culture and history of their Dragon Age incarnation. Outside of games with a lot of elaborate body customization, I've never seen a human woman in a video game that looked remotely like me. I probably never will. I don't blame BioWare for that - I don't expect them to overturn the conventions of the entire entertainment industry on my account. But if I can play a woman who's short, curvy and muscular via selecting 'dwarf' at character creation, that makes me happy. (I would also love to play a fat woman in an RPG some day, but I do not expect miracles. Maybe body sliders will become more of a thing in the future.)
Well, I can relate that I haven't seen a human woman in a game who looked much like me, except some I've created. Because of how many body sliders there were in Neverwinter (not Neverwinter Nights), this is the closest to my body-type any of my characters have.
The other thing I like to do when given body-sliders is to simply make larger-framed, muscular women, since that never happens otherwise, and usually makes more sense.
I really hope/wish Bioware would implement them. I know they would cause a lot more work for animation, but I think it would definitely be worth it. Remember, this would apply to all characters, not just the protagonist, so I think it would go a long way in making the world seem more real, since people in real life actually have different bodies, not just faces! *Gasp* 
If they won't do that, I think they should at least implement a range of (maybe 3) preset bodies so we aren't stuck either being an incredibly jacked lumbering brute as a male, or an unrealistically un-built supermodel "soldier" as a female. Keep in mind that for Andromeda, which is human-only, this would be less animation work than making 4 races was for DA:I, and significantly easier since the bodies would be much more similar in size.
Now onto the mage part. I am someone who inherently likes to learn, read and study things. I have been doing this for as long as I can remember and I do it to the point where people now tell me (I'm 25 now) - "There's no point in you studying so much. You should be working hard,saving money, get a girl and start a family." FFS, when I was in high school, my parents stopped buying books for me read in my leisure time because according to them I am reading too much and costing them too much money.
Wow, that sucks. I never got anything but encouragement for wanting to learn. Sorry 
Long story short ... because I am denied such a choice in so many other games. While I have no particular issue with Human Characters, being forced to play them in so many other styles of games (especially RPGs) have made them all around pretty boring. They are the status quo, the mundane, the common. Playing characters of other races feels a bit more unique, if only on a surface value and if only because now I have a choice.
Though I normally define what race i want to play based off of a planned theme for a character rather than anything else anyway, so if the theme calls for a Human, I'll gladly play a human.
I can totally understand this, because if you replace "human" with "male", I could have written almost the same paragraph 