Deadpool is not cured of his cancer. When he gets his healing factor, so does his cancer, becoming super cancer. His healing factor fights it at an accelerated rate, but neither wins. Hence his face. And anti-telepathic brain. And insanity.
The cancer is just mutations in normal cells. Wade is genetically predisposed to it, so the healing factor can't stop it from happening. And since the cancer has his DNA, it has the new healing factor too. He can't just cut out the cancer, as new cancer cells spontaneously mutate everywhere.
His skin, like all his other internal organs, including his brain, constantly get cancer, which the healing factor fights off before they can become fatal. It changes how his skin looks often, and how his brain is wired. Since his brain isn't normal, and constantly changes, it causes him to be immune to telepaths.
His cancer wasn't cured. It was deadlocked in a never ending battle. Somewhere in Volume 2 of Deadpool comics, Daniel the hack Way wrote that removing the cancer without removing the healing factor will lead to the healing factor overcompensating and killing Deadpool, as it did the Super-Skrulls that were given his healing factor.