But yes, I think a lot of people would say there should be a cap on how much more wealth someone has compared to the median, for many reasons, such as the amount of political power it would yield him. The thought experiment uses a harmless activity for earning the wealth, but criticism of wealth inequality is often based on what happens _after_ the wealth is earned too. If in this example you will claim the world remains perfectly (socially) egalitarian and the kid will be benevolent, then maybe we can let him keep his wealth in the thought experiment. But that’s not the world we live in, and possibly never will be.
IIRC, that's precisely what Nozick is nominally interested in exploring (although he really doesn't).
There at least 2 distinctions going on:
1. whether wealth is acquired with or without exploitation; Nozick uses consent as a proxy for exploitation, which is dubious but predictable given that he's a libertarian
2. whether there are ill-effects to (excessive) wealth regardless of how it was acquired
Which one is the better allegory of modern capitalism?
It's about how a utopian society could and/or should respond to changes in resource distribution, and how entirely consensual behavior and exchanges between people can still lead to situations that are problematic.
Making everyone have the same income means there is already a big infrastructure to manage how resources are allocated in this society - it already can't have been a free-trade system with currency that can be arbitrarily sent and received.