What is the function of oil in baking/roasting?
(Liquid) water cannot exceed 100°C because that it's boiling point, and any additional heat applied goes toward the latent heat of evaporation needed to turn it into a gas (steam, which can then be higher than 100°C).

Oils have a boiling point much higher than water, and a point lower than that (but still much higher than water's boiling point) called the smoke point which you do not want to reach (as it causes dangerous break downs of the oil).

Oils aid in crisping by facilitating heat transfer. They are liquid so they have good coverage, and they sort of "stick" to the surface of the pan and the food. Excess drips off, but there's still a layer.

This layer has good coverage so it provides more contact between the food and pan, facilitating heat transfer.