Lol 6 isn't huge. It is baseline. For instance if every child wants to be able to use the phrase "my brothers and sisters" 6 is the minimum number where that is possible.

It is not, however, a guarantee.

Furthermore if you want to be reasonably sure that your surname will survive every generation of your family needs to have at least 5 kids. 95% likelihood.

This is equivalent to estimating the survival of your genome since you only pass half of it.