Cancer is primarily caused by aging, so in this world there likely wouldn’t be much cancer outside of the deliberate cancers caused by things like smoking
This is grossly wrong. "anti-aging" treatments won't reduce people's ages and won't undo epigenetic damage. And while age is the single strongest risk factor for cancer, it isn't the "primary cause", and there are numerous non-age-related causes of cancer.
Bad “anti-aging” treatments definitely won’t do it, but they also won’t provide indefinite lifespans.
> it isn't the "primary cause
Only if you’re using an inaccurate definition of aging. If everyone over 20 should have the same risk of cancer as 20 years olds the total number of cancers would drop by more than half.