If these fictional races are so alien we cannot understand or feel them, then how was Bioware, who consists entirely of humans, able to create them in the first place? If a writer can get into the alien's mind enough to write them, a player can get into their mind enough to roleplay them.
The problem with your statement is your impression that BioWare has done a good job of creating these aliens. Truth be told, they have not with most of these aliens. Examples of hanar, elcor, and rachni are aliens who actually are quite unique and do provide a very different perspective from the humanoid turians, quarians, salarians, krogans, and asari. Of course, it is the latter aliens that are more popular because people don't realize they subconsciously prefer aliens who are more relatable because they are virtually humans. The fact people even call for relationships and romance with these aliens shows little distinction between an alien and a human.
Again, by trying to make another alien the central focus of the story, you merely will humanize it and take away what makes it alien in nature. As I've already stated time and time again, Mass Effect is about the human experience and how it views these various lifeforms in the galaxy. To get rid of that understanding is to shred away what makes Mass Effect what it is.
That's only because Bioware took everything that worked in DAO and threw it in the trash. They tried to make Dragon Effect with DA2, and were probably continuing full speed ahead with the next game when the backlash hit. It didn't work because multiple races are bad, it didn't work because the implementation was bad.
Except, multiple races didn't even really work in DAO. In fact, the origin stories were incredibly impractical, difficult to implement, and thus BioWare will never do them again because it severely limited what they could do in the rest of the game. The various races virtually didn't matter after the origin story because all of the specialized content happened at the very start of the game. DAI tried to avoid that by providing specialized content for each race throughout the game, but it still did not work.
Whether it would work or not really isn't the question. The point is BioWare should never do it well because it's too costly and other areas of the game would suffer for such a focus. Not to mention, Dragon Age is much more about the various nations and less so about the particular races in play. The inclusion of dwarves, elves, and qunari did little to improve DAI, especially considering each had such a minuscule effect on the game.