The facial recognition is not the real problem.

The real problem is things like gait recognition. Most people already cover some or all of their hips, legs, feet, etc.... But it's hard to hide the way that you walk, regardless of what clothing you wear. And even if you can fake it for a short period of time, it's hard to be consistent about how you fake it over a long period of time.

When you can accurately identify the person who is completely covered head to toe, then it becomes a lot harder to hide.