In the not-so-distant past, the term "desert" would have included what is now referred to as grasslands, savanna, or steppe environments.

Anyway, there are 10 states in the US with a lower pop density than the least densely populated country in Europe (norway, which is already quite empty). Half of the US states have less than 40 inhab per square kilometer. Sure some are farm land but it's far from all of it https://map.onesoil.ai/2018#3.89/38.32/-98.67