I think the problem is that there is a difference between the Icon field and a field with the name Icon.
As an analogy, if you create a field called State, you won’t be able to add the Workflow field, since it has to have the name State and that name is now already taken. This doesn’t mean that the field you created will function in the same way as the native workflow field.
Similarly, if you define a (formula) field called Icon, you are prohibiting yourself from using the native Icon functionality, but the field you created will not behave as the native Icon field does.
At the moment, there is no way to define an icon using a formula, sorry