Graded exposure can be a more manageable way to get to the end result (fear extinction), but reminding yourself that the threat isn’t real is a fear-neutralizing behavior that will limit the effectiveness of the treatment. The point of exposure therapy is to feel the fear and to do nothing about it other than let the feeling (eventually) climax and dissipate. (In fact, “lean in harder” can be even better than “do nothing”.)
[Edit: I want to emphasize this point for others who may find this post: if you are doing exposure work or you’re supporting someone who is, please don’t reassure yourself/them that the exposure isn’t dangerous. At best it undermines the treatment; at worst it reinforces the fear. When you violate your anxiety by facing a feared situation or idea, it will and should feel like you are doing something bad and dangerous.]
Second, graded exposure isn’t always necessary - flooding (direct exposure to the high level fear situation) works too, and can work a lot faster.
But I think most people with anxiety disorders have a number of fears not just a single isolated phobia - and they’re connected in a network of sorts. It’s often helpful for the person to experience success in extinguishing a low-moderate grade fear first, to grok the process and build confidence to approach their worst fears successfully.