That's a little simplistic and forgets one thing: natural selection only cares until you're old enough to procreate, biologically, and there's nothing it will do for humanity after that age.

So yeah, natural selection is totally cool with you dying of a splinter at 16.

Sorry to bust your eugenics bubble.

Like a genetic mutation that makes you sicker

That's 1918 thinking.

Natural selection is driven by pressures that affect reproduction chances

Oh, like dying of old age at 28 of a broken foot or a fucked up tooth?

Like a genetic mutation that makes you sicker

In nature it's what cleans the genetics of a species of disease over time, preventing infinite accumulation of negative mutations

If you think that's all that natural selection is, you're woefully uneducated on the topic. Because natural selection does in fact include external pressures like predators, disease, and accidents, along with genetics. Genetics can absolutely make a difference in making it to reproduction, but environmental factors are just as big of a factor, if not bigger, in making it that long.