My biggest concern is that a good competitive game should be as much about skill and knowledge and as little about randomness or luck as possible. I'm not saying that we couldn't run a competitive game without species clause, but I think the competitive nature of the game would be significantly reduced by such a change.
Why? Because facing 4 Garchomps means each time they switch in, I have to guess which set I'm facing and try to counter. If I'm facing jumpman's Lucario team, the guessing game increases even more. Salamence? Specs? Banded? Mixed? It makes playing the game, choosing moves and making changes more about random guessing than is does about calculating risks.
That's not a good competitive environment. That's chaos.
In the current metagame, your opponent basically has one chance to surprise you with their set. You have the opportunity to scout or make an educated guess, but if they surprise you with something original or tricky, you have the chance to identify the set and build a strategy to compete. Despite all of the random number issues, crits, etc, etc... this basic system makes Pokemon a solid competitive system.
If we remove species clause, yes... it will be POSSIBLE to counter their team and get an easy win in some instances. However, for the most part, the game would devolve into a guessing game. Do I attack with special or physical attacks? Do I need to use a priority move to hit you before you throw up a sub or do I go for a SE attack for more damage? You can't make much by way of educated guesses. You're just guessing. That's not a good competitive game at all.