Why do drones use Li-Po instead of Li-Ion?
For this answer I'm going to define LiPo as flat packs, and Li-Ions as 18650s. The reality is more messy than that, but I believe this way of defining the terms will help answer your question as you seem to have intended it.

Traditionally, 18650s didn't support high current applications, a continuous current rating of 5A was considered to be high. 18650s that support 20A continuous current were more or less unheard of until high power cells like the Sony VTC3 came on the market. 

(As a general rule, 18650s that claim to support more than 30A continuous, even today, are simply overrated. There is also a trade-off between capacity and continuous current capability; For example the 30A Sony VTC4 is "only" 2100 mAh.)

A lot of the reason why drones use lipos are probably tradition, due to this.

When you say that LiPos have a lower energy density, you mean a lower energy to volume ratio, right? I'm pretty sure they have a higher or at least as high energy to weight ratio, as Li-Ions. 18650 Li-Ions have a metal casing. That's unneccesary weight.

The flat form factor of many LiPos probably also helps with cooling.