While truly alien aliens are cool, they are also hard to write into the story like mass effect. Or at least as anything but npc's you dont interact much. For example how would they work in a squad? The reason why we get humanoid aliens as squad mates and friends is also because they are easier to relate to. Writing a believable interaction between truly alien aliens and humans is hard and any meaningful interaction with them would be limited.
Solaris(the book but I guess the movie works too) explains it a bit. And really ME is one of the better examples of scifi with believable aliens that you can interact with. I have read attempts by authors to create truly alien aliens and stick them in situations where they have to interact with humans, most of those are disasters.
Legion in ME 2 was a squad mate that held rather a 'alien' perspective about the setting. What he talked about wasn't something incomprehensible, but neither was it something that we as the human audience could immediately relate to, and that was a good thing (IMO). We were able to see how something with a completely different frame of reference on the universe acted; we were able to see how this alien society thrived despite being nothing like our own civilization.
Using a non-humanoid form is not necessary for a truly alien species to function; though it does help to further sell the 'otherness' of the species in question. I will admit to a preference to aliens like the Rachni, as I really enjoy the concept of incectoid aliens, but their unique way of talking, their hive mentality is what helped shaped them into one of the few 'alien' aliens of the Mass Effect setting.
<Slightly off topic/rant-y>
I would love to see a full fledged, non-humanoid alien as a companion; a Rachni, Hanar, or Elcor fully animated and 'realistically' depicted in the setting. Personally, if I were BioWare I would devote less time trying to reinventing the wheel with new human animations and mo-cap sessions and instead devote my animators towards bringing the non-human elements to life. You would think that the sheer amount of human animations like walking, running, jumping, etc. would have already been done by someone. There is a huge library of human animations, rigging skeletons, models, etc. that BioWare can pull from from other Frostbite games like Battlefield, or even Dragon Age: Inquisition that can work just as easily in Mass Effect: Next.
Every game out there that deals with us humans does animation work on our myriad of motion and movement possibilities, but how many games out there have that same level of quality towards the non-human side of things? If nothing else, having a fully fledged non-humanoid companion would at least help BioWare stand out from the crowd.