I would also wager that a HEAT round is cheaper and easier to manufacture than a APFSDS round. Maybe that influences the decisions.
Other influences may include
If APFSDS rounds are fired from rifled barrels, it causes more wear in the barrel. This is due to the need for a "de-rotating" sabot to keep the kinetic core from spinning. A spinning APFSDS round won't travel as far and will have decreased accuracy. This is one of the reasons APFSDS rounds are usually fired from smooth bore barrels. The advantage of HEAT rounds is that it can be carried with other tank rounds that need rifled barrels.
The core of a APFSDS round is expensive and difficult to manufacture. Working with either Depleted Uranium or Tungsten Staballoy is not was easy as manufacturing a HEAT round.
There is an ongoing debate concerning the use of DU rounds.
Although this is probably not a big concern to the big brass, but it must suck being Infantry and having your forces firing APFSDS rounds from behind you. Them sabots have to end up somewhere. The Sabots, upon separating from the core, will continue down range a few hundred meters. Bouncing off the helmets of the Infantry guys in front of you. Ouch.
Lesson 1: Don't be in front of a tank firing APFSDS rounds
Both rounds (APFSDS and HEAT) have their advantages and disadvantages. I don't think one is clearly always better than the other in all situations.
Now if you want to talk about HEP rounds (or HESH to your Brits)... That's innovative technology