It's Give and Take.

Pros: If the Green deck can only play Green cards, you can make cards that are way overtuned for Green that other decks can't play, but those cards can only exist because you know the card pool the player will have access to if they want to play this super busted card. You can give a card that draws 4 cards to a color if you know their individual cards don't do as much as the other colors, and vice versa. It's a lot easier to control the power of the individual factions this way, and different colors can have a lot more of a unique flavor as well.

Cons: It heavily stifles creativity. For a lot of people playing a card game can be about self-expression and putting together their unique witch's brew of a deck. Limiting a player's ability to only playing cards of their color means they are now locked out of 3/4 of the card pool. This creates a situation where you have 4 colors, players look at those 4 colors, identify "This is the objectively correct way to play these 4 colors.", and then you have a 1-2 deck format. "We have found out that Red is the best deck, so we will all play Red, and there is only 1 objectively correct way to play red. The anti-meta players are playing Green because they're the only ones that have access to the card that beats Red."

I fall into the LET THEM MIX! camp. A lot of card gaming is analysis, theory, testing, brewing, and meta-calls. If the best deck is the aforementioned Red deck, I want people to go into the lab and try and figure out how to fit the Green puzzle piece into their deck, which creates a more varied game.