Ah, yes that makes sense...I did something similar in the early days of development, but then I changed it so that AP is only used for movement in my project. I simply made it so all skills/actions don't cost AP, but they are limited to a single skill per turn as a result. Then I added something called Bonus Actions, which are things like buffs and utility skills, which don't consume a turn but can only be used once before the Main Action, per turn.
The reason I didn't want to scale actions w/ Speed using AP is cuz the "levers" are too large. As in the minimum difference between a faster and slower unit is at least an entire action, if not more in most cases. So having units that can potentially act several times per turn vs another unit is pretty imbalanced, imo. That's why I relegated AP just for movement lol.
But yea, there are lot's of ways to approach it. That's why LTBS is so awesome cuz it's so flexible!
Edit: Also, I felt that having movement and actions using a shared resource (AP) makes it so ranged units are at an advantage and melee units are at a disadvantage.