Naturally, a high magic world would be a high counter-magic world.
But equally naturally, as that started to increase, wizards and anyone else who used magic would favor magic that constitutes area attacks not directly affecting the person protected from magic. Use fire to heat up the scene and suck up the oxygen. Knock down the building on your head. Smash the floor under your feet. Flood the scene.
And after that, wizards and other will work on counter-magic that extends for an area.