Yeah, water floats and gravity is gravity. But in the end there is the physics on one hand and the performance on the other hand. I never wrote there will be a distinct advantage for recreational sailors, but from a physics point of view it is easy. Everything else equal a lighter board will easier to move around. A quick cutback is a very fast rotational move as far as the board is concerned. If the board is 20% lighter, you will need 20% less energy to make this move. And if you really put a good experimental physicist on it, of course you could measure it in practice too. I'm the first to say weight is not THAT important in a wave board, but when you sail the same shape in two different constructions you will feel a certain difference after all. But the beauty of it is that any customer has the choice. Nobody is forced to buy a more expensive carbon board. Wood and technora works great.
In slalom, a lighter board would be theoretically better because the board is continuously accelerated up and down by the chop this soaks energy from the forward motion. But this is theory and in practice things like comfort plays a huge role and if test show a carbon board is not faster, then theory will not matter. Even in moto racing the suspension is not tuned for maximum power transfer but for a compromise of power transfer and control/comfort.