If the content were balanced around not having Lost Actions, then that would unbalance the content even more when some have them and some don't. It would be a repeat of "I missed out because it was dead before I could get there ".
Either the content needs to be balanced around the existence of Lost Actions, or Lost Actions would need to be removed altogether. Remove the Lost Actions, and you remove what makes the content more interesting than normal FATEs to many players.
The Lost Action system isn't a borrowed power system, though. Lost Actions are consumable buffs. They'll still be available for you to use in Bozja/Zadnor next expansion if you go back to level up new jobs or farm relics you don't obtain this expansion.
But I do agree that borrowed power systems like those in WoW are terrible. No point in putting in all that effort if the reward is going to be permanently taken away from you at expansion's end.