I used to have my ankle taped when I first blew it apart in high school.

The reuseable wrap is lighter, more comfortable, and cheaper to use. Further, I can redo it when swelling increases or decreases.

So, I think taping your ankle to regain mobility after an injury is an option, but it is a heavier, less flexible, and more expensive option.

That said, a sports medicine expert might have a different perspective.