There are more efficient amplifiers than a single MOSFET in linear mode. For instance a push-pull amplifier is much more energy efficient, at a cost of linearity.
Aside from CRTs, most outputs use a low power DAC and then an amplifier. This way your DAC doesn't go out of calibration from heat, and the amplifier transistors can each have their own heatsink. I've looked for power amplifier ICs, but have not found them. I think that an IC package is just not suitable for power dissapation.