You didn't twist your ankle because it wasn't strong enough. You twisted it because the perception-action coupling was weak, and your sensitivity to it became too slow (to the situation). You allowed your body to enter a compromised situation and harm resulted.
One mark of an excellent athlete is the ability/capacity to sense they are on the verge of hurting themselves – and pull back before injury happens.
But actually, both of these – sensitivity and strength – are false. Monocausal explanations almost always are. Sensitivity is closer to capturing the underlying complexity, but of course many factors shape the situation, including the strength of our ligaments. [We are complex systems].
What causes wind to blow? Is it the opening between two mountains, funneling the air? Is it the temperature difference between layers of the atmosphere? Or the sun that causes the temperature difference? Causation is a story we must tell at several levels. Our body is no different.
Strengthening exercises in practice (in my experience) are less useful than improving the coordination of your body, and the sensitivity of your balance, proprioception, and interoception.
Avoiding injury more effectively should mean more sensitivity and coordination as much as mobility and strength.