IMO our goal shouldn't be for everyone to be objectively equal in all ways, but rather to be provided enough resources and opportunities to live a good life.
Like on the opposite end of your example, if I was born with a congenital condition, or became injured, I should still be able to live a good life with my needs met and opportunities to do good work. The fact that we don't have that today, due to lack of a social safety net and accessibility, is a problem.
That's an absurd comparison. Children of parents who are poor and don't have connections can still compete, but simply cannot benefit from their parents trafficking influence.
If you really want to go with a sports metaphor, your example is like barring children from having a fair shot at sports because their parents aren't rubbing elbows with the coaches.
children of parents who don't have inheritance can still compete economically. So no, it's not an absurd comparison between inherited wealth and inherited genes.
what about the children of parents who has good genes? If a child is athletic/healthy/good-looking, because their parents had good genes (and the good luck for a good combination), do you also resent that the child has a head-start?
parents helping the children get ahead is natural, and should be encouraged imho.