It uses up valuable time, and the contestants & chaser can just find out how much they got correct when it's over or looking at the scoreboard during the game. Imagine how much more they could potentially get if you didn't have the host saying correct after all the right answers. Especially in the earlier series when Bradley used to say 'Corrrrect' sometimes. But back then, he also read the questions a bit quicker than recent series I'd say.

And if the buzzer press was just a press that showed a light to signal to answer instead of waiting for the name which can use up nearly a second of time. That's what they do on the chase Spain and I think that is much more time efficient.