Well, BJT are not linear too, that's why we usually add a negative feedback path.
MOSFETs have a huge gate impedance which is useful in many occasions. Also their distortion behavious is… well different. MOSFET also need a lot less bias current so they are useful in battery applications.
As discrete component you almost never use a mosfet amplifier at low power (except in special cases, like some RF applications). However in power circuits it's a different story, efficiency it's usually better.
The real importance of mosfet in linear mode is in IC design where the process simplifies mixed signal design (logic and analog on the same chip). When you use opamps these days you are either using a mosfet amplifier or some hybrid (like BiCMOS processes).
Both MOSFETs and BJTs (JFETs, too!) have their use in both low power and high power applications. It's just that discrete designs are not prevalent these days.