Give up the permeability a core provides and you get something a ferrite part cannot offer at any price: inductance that does not change with current, and no core loss at frequency.
Inductance
Current
Air core — flat to the thermal limit
Ferrite core — saturates
Inductance holds from zero current to the thermal limit. There is no core, so there is nothing to saturate and nothing to move with temperature.
No core loss either, so Q stays high at frequency where a ferrite of the same value would be heating.
The cost is permeability. An air core needs far more turns for the same inductance, so it is physically larger — which is why it is specified where linearity matters more than size.
Air core against a ferrite core of the same nominal value