I believe that all weapons should be able to throw. Even if the heavier ones don't go as far and less strong throwers don't achieve the best effectiveness.
As for throwing axes I use them with a character that fights on foot and they are very effective if you can aim well and have a high throwing level. Only the aiming and throwing speed is too slow to be able to throw all three units. Then you have to change the weapon or change the functionality of the weapon by converting it into a melee weapon. In this case it is a very fast but very short branch but it is also functional.
I think the problem is not so much in the weapon itself but in the concept of use in the game. If the use of the weapon was based on the sum of the character's skills, height and physical strength, and all weapons could be thrown, the game would be different. But that's my personal opinion