Because Wade’s cancer (like every part of his body) inherited the same DNA, any mutant genes — and superpowers — would be activated in his tumor cells too. Deadpool would have a super-cancer. Those malignant tumors would have already defeated every weapon his super-defenses had thrown at them, so his body’s normal immune system wouldn’t stand a chance. Wade Wilson would probably die within hours.
Deadpool’s healing factor is therefore a double-edged sword as his superpowered cancer cells could succeed were blades, bullets and even bombs have failed: it would finally silence the Merc with a Mouth.