Why would PvP make you pay attention to Pokémon that aren't good attackers? In the absence of a system that forced you to use certain Pokemon, I'd imagine that most PvP would break down into a Rock/Paper/Scissors game where you had only the strongest attackers being used or their most optimal counters being used.
You're about to battle someone, do you bring in a Machamp in case they bring in a Tyranitar? Or do you expect that they are going to bring in a Machamp to take down your Tyranitar, so you bring in your Mewtwo, your Lugia... or maybe your Gengar? (Triple resists Fighting!) Etc.
While I can see PvP adding to the game, I don't see how it would make someone pay attention to a Pokémon like Steelix, or even Ursaring. It seems to me that it would instead just follow the same lines as Raid Battles, where you hyper-focus on the most optimal counters to Raid Bosses rather than going for more interesting matchups (Clefable vs Latios?).
While I wouldn't mind PvP, I'm not sure how it could do anything more than accelerate the current trend to hyper-focus on Attackers, which I think is the main mechanical issue with the game as it stands.
Maybe if it was a 1 vs 1 Battle, but you had 3 Pokémon on your Bench which you could swap out during the match? Maybe 1 switch per match? So you bring a Machamp, a Mewtwo and a Tyranitar, your opponent brings out a Machamp, a Rayquaza and a Gengar, and the match turns into Mewtwo vs Rayquaza? It's still Rock/Paper/Scissors, but at least it's a bit more varied.