As I said in another thread, I think that Trek has gone past the TOS-era paradigm where it was basically an anthology with a regular cast, which could tell nearly any sci-fi story imaginable. A large portion of Trek has become the corpus of lore - if you ignore that, there's barely even a reason to have a given episode take place in Trek at all. It would be like running a D&D campaign - if you're using Forgotten Realms, it's precisely because of the huge mythos which has developed over the years - otherwise you would chose a different, more generic (and possibly free-form) setup.
As others have said, the main issue with aliens of the week is they aren't - well - alien in the slightest. Forget about having a point of view which would seem odd to a human, for the most part they are completely indistinguishable from late 20th/early 21st century Americans - unless they have "one weird trick" which is the crux of the episode. Voyager was by far the worst example of this, but all of the series did it to a certain degree. Now I know that you couldn't do a truly alien culture justice in only a single episode, which is why unless the episode is legitimately about the difficulties of first contact (like say Darmok) they should be avoided - to allow greater nuance and depth. If you want to just have rando characters as plot devices, use humans or established races.
The other problem with new races is often you just travel the same path that has been ridden before. I'll make an extreme statement here, but one I will back up: the Cardassians were a mistake. Don't get me wrong, I love what DS9 did with them - they were given, by far, the best development out of all of the "antagonist" races in Trek (arguably the best development period). However, there was no reason for the Cardassians to exist. I say this because the Cardassians and Romulans were very similar in basic psychology and their empire structure (right down to having nearly all-powerful intelligence agencies). You could have had Bajor suffering under Romulan occupation for decades and had the series work out roughly identically. Of course, creating the Cardaassians did no harm in the longer run - except that the Romulans were more or less abandoned as a focus race through the remainder of Trek, meaning they were never fleshed out beyond being some secretive "hermit kingdom" kind of state. I'd worry about the same with introducing "new heavies" - essentially they'll just fall into either the Klingon or Romulan/Cardassian archetypes eventually, telling stories that could just as easily been told within existing lore.
