Well probably no, they're probably not respected enough. Which is why I said earlier that I wouldn't be so harsh on a requirement for a BFA.
Like I said initially in response to the idea: In general I'd like to see people with better backgrounds in art history, critique and writing skills. The stuff you read from "reviews" is often of such a poor quality, filled with poor writing techniques that my high school English teacher would have ripped me on. Let alone what kind of quality a "professional" critic should be putting out.
In regards to stuff outside of the "game-ness," I agree to a certain extent. I would personally still like there to be at least more "artistic critique," considering things like aesthetics, themes, narratives, etc (although it doesn't need to take over the entire critique scene). There are enough games that are doing narrative focuses and "indie art" spins that we could use more people exploring that stuff (I'm guilty of a personal bis here though because those are the kinds of games I love the most). Hell, I'd like to see more people critiquing that stuff just to push devs to do more so that we can evolve beyond the garbage writing present in 85% of games. So a better understanding of art history in other mediums (film, TV, literature, painting, etc) would be excellent foundations for that kind of critique.
But more importantly, I'd like to see critics having a better understanding of the art history of their own medium. There's such a huge gaming illiteracy issue among professional critics that it's mindboggling. And yes, before someone jumps on this, there is value in having some "outsider" opinions. But that shouldn't be the majority of voices in the professional critic circles.