You could, but gearboxes are a source of inefficiency. And expense, weight, and mechanical complexity.
In fact, electrics in RC went through a long phase where motors were almost invariably bolted onto gearboxes, and almost invariably spun in excess of 15000, or even 20000 RPM.
"Outrunner" motors such as are used almost exclusively now were specifically designed to generate a healthy amount of torque at lower speeds, to obviate the need for a gearbox.
Edit:
I misread the question -- I thought you wanted to know why we don't use gearboxes anymore, not that you wanted to know why we shouldn't gear things up.
For that -- Brett's answer.