One problem off the top of my head is run-time changing of components. An entity that inherits from multiple mixins can't inherit from new mixins (or lose existing ones) at runtime.
Nothing in the "Inheritance isn't Always the Best Tool for the Job" section talks about runtime changes in behavior.
> Most object-oriented languages are designed so that an object's underlying type will be the same for its entire lifetime. This makes things interesting when users want to scale a Circle without maintaining aspect ratio.
Mixins simply fix single inheritance so a subclass's parent class is parameterized, and so concrete classes can be composed of several non-related mixins (which will often seem like multiple super-classes).
ECS is a much different and bigger beast. It's a runtime composition pattern, and has almost basically to do with classes or objects.
If you're only complaint about OOP is with single-inheritance, ECS is probably overkill.
Is it the fact that (some implementations of?) mixins' members could collide and conflict with eachother?
Your 3rd paragraph, did you miss "nothing" or perhaps another word?