This is today's thoughtful cartoon by Zach Weiner on the relevance of genetics in our motivations:
The main fallacy is that inbreeding, at least some inbreeding, does happen.
The other fallacy is that some 99.5% (exact figure anyone?) of the base pairs are identical among all humans and highly conservative (they won't change on risk of death or otherwise extreme crippling), so the time to your total genetic dilution (notwithstanding inbreeding) is a lot shorter that Weiner assumes.
Actually I estimate 150,000 variable base pairs, so following the cartoon's logic, only 18 generations would be needed to total dilution, so only 450 years are needed for (theoretical) total dilution.
I was going to illustrate this talking about some random person from Columbus' times... but in that time Earth's human population was low enough to allow some of that almost necessary inbreeding of the sort suggested in the cartoon. But now? Now there's more people on Earth than all the base pairs in our genome! Now such necessary inbreeding cannot be taken for granted and will probably not happen in most cases.
Carpe diem (live the day) or just discuss?