a symbiote may have started its evolution as a parasite infecting a host. After millions of years of evolution the two species, host and parasite, may have developed a symbiotic relationship with one another. it is very possible that there are other species that have this type of relationship. Trill are the most popular blended species in star trek.
What are the chances of a succesful permanent blending with an alien? You may find a suitable candidate, but maybe the host gets the a flu and it kills the symbiote. Or vice versa do do some weird interaction with the symbiote.
I agree that the sybiotes and trills have evolved to the point of perfect blending. Why risk possible death unless absolutely necessary? And even then, just do it for the temporary until you get to a trill.
Maybe I am reading this wrong, but perhaps the OP is suggesting Aliens with non-trill symbiotes. Surely there are more symbiotic races out there besides Trills, but as Omega said they won't be unique anymore, like a lot of the racial skills.