We've established that the body is necessary for the imperfect happiness of this world, because it can be tied directly to senses, which perceive the physical world. However, the body is not necessary for the perfect happiness of the afterlife.
Perfect happiness comes in the vision of the divine essence, as Aquinas states several times.
But, we cannot perceive the divine essence through the use of our senses. It's hard to come up with an example of this, but perhaps we can look to the mathematical world. Mathematics is, in its complete form, abstract. At that point, it becomes more intellectual and less reliant on the body.