Telomeres were also just a theory, based off observations of older people who aged well, and other species. That long telomeres prevent the cell damages as they act like a sort of redundant absorption for mutations. However, much like the DNA damage theory, it had a lot of conflicting evidence that made direct correlation hard to prove... It's likely long telomeres are more likely a symptomatic correlation rather than causal.

Tumor suppression probably also exists within the epigenetic side of things as well. As we age, our bodies get worse and worse at fighting things off. They replicated this by artificially aging the mice which suddenly got more tumors. So as the epigenetics of the cells get more noisy, so does their ability to precisely work as intended, thus more tumors.