think of it like a game of "monopoly"
would you participate in a game where your competitors already owned hotels on half the board and had vastly outsized cash reserves before you even rolled your first move?
forget the metaphor for a minute
would you play this board game ?
This presumes that any utility I derive from my skills and labor and the fruits thereof is necessarily a competition with that of others. One needs not be "the best" in order to do one's best.
As for whether I'd play the game, in a competitive context, no I would not.
pLEASE eXPLAIN
Your previous statements in some manner inform my contention. That is, the idea that everyone should have the same shot at the same outcome (equal opportunity) as opposed to the notion that everyone should go as far as their abilities can take them. In order to set things equal, even just to start, one would have to eliminate private decisions especially those which inform advantages.
So let's use nepotism as an example:
Say I'm in the market for a babysitter. I meet a candidate who has a Ph.D in both child psychology and child education. She has years of experience and she had numerous reviews which raved about her. She is sure to be a lock. Just before I finalize my decision, my 16 year-old daughter expresses interest in being a babysitter. Ultimately, I decide to hire my daughter because she's my daughter. So if we were to maintain ANARCHY = EQUALITY = NO NEPOTISM, then that would undermine individual interests particularly the ones which concern said individual.
Now let's change this up a bit: let's say my friend is in the market for a babysitter. He delegates the task of finding a babysitter to me. I meet the same Ph.D candidate and my daughter expresses the same interest. In the end, I recommend my daughter because she's my daughter. My friend agrees to hire my daughter as a favor to me. Once again, to undermine this would be to undermine individual interests.
What about a pretty woman? Do we tag her up a bit, so that the uggos have a "fair shot" at a modeling job?
ANARCHY =/= EQUALITY; ANARCHY =/= NO NEPOTISM; ANARCHY =/= NO ADVANTAGES. Anarchy is poitical/social individualism, which would delineate that in spite/favor of nepotism, inheritance, and social/economic advantages, as an individual, your life is a function of service to your own best interests; that your talents, skills, abilities, labor, time, etc. are yours to do with in whichever manner you see fit, so long as it does not infract on another individual's capacity to exhibit the aforementioned. Nepotism and inheritance are not infractions.