Animals don't drop dead left and right - in the wild -from cancer because they typically die before cancer grows. Cancers generally grow pretty slow. You don't go from 1 cancer cell to 2 billion in 6 months. It typically takes a long time. Animals raised indoors do get cancer at a fairly high rate.

Though not as much as humans. The diet factor is a huge part for sure. Virtually all the major bodies like the UN agree on this.