Comment by spauldo

A light oil has a density of 700kg per cubic meter. Most common oils are denser.

Then you'd need vanes, agitators, and pumps to keep the oil moving around without forming eddies. These would need to be fairly bulky compared to fans and fan motors.

I'd have to see what an engineering team came up with, but at first glance the liquid solution would be much heavier and likely more maintenance intensive.