HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

The problem is that sometimes a person isn't just thinking strategically, but is simply moving golems around the map, and it's strange that they should be penalized for this by having two or three units miss their turn.

That's right. And if they're moving them with a ballista, it's even more absurd. Everything should have a cost, even if it's in this way. Following your logic, you should play with unlimited movement points so you can do everything perfectly. I, for example, think that moving the hero around the map is more important than battles.