It is interesting--most Sci-Fi stories promote Alien characters that are also Primates/quasi-Primates.
No they don't. Of those which do promote such characters, it is usually due to a lack of imagination on the part of the creator. I mean, let's be fair. You have conducted no global historical study of alien characters in sci-fi stories. You decided to use the word "most", purely to create the (false) impression that you are a form of authority in the matter.
However, this would seem highly restrictive to what the true spectrum of possibilities is.
Of course, but your initial premise is false in the first place. Aliens are presented in science fiction as anything from giant robots to small furry rodents. Primates however are creatures which have evolved on Earth itself as a direct result of the environment they have been living in. Every biologist will tell you this, were you actually to ask any of them instead of simply deciding what they believe for yourself.
Although, there have been some Biologists that have argued it is very reasonable to suppose a quasi-Primate form for 'advanced'/'intelligent' extra-terrestrial life
Biologists can't tell you if life exists on other planets or what form it will take if it does. They are every bit as clueless as everyone else because biologists study life on Earth and only life on Earth. The odds of life developing the same way on two different planets are astronomically low, unless of course the seeds for producing what happened on Earth are floating around elsewhere in space: a scientifically backed idea which you once spent three entire weeks childishly mocking me about because you were upset I challenged your perceived (i.e. non-existent) scientific authority.