Equality of opportunity kind of ends up being equality of outcome. I understand that it can be defined in narrow, libertarian terms, but rhetorically, this is how I always see the argument going...
None of us are born with the same opportunities in life. We aren't born as smart, as strong, as attractive, as rich, in a location with the same opportunities, to parents who invest in us, or with inclinations that society is equally able or willing to cater to. Life is inevitable a game of poker where some people come to the table with more chips than they can carry, while others have to borrow chips just to play. To get people to the table with the same number of chips, you are already engaged in the same cosmic battle to level the playing field that the equality of outcome folks are involved in.
To achieve what they want, you need to remove the game of chance completely
I think equality of outcome is a bad goal, but in choosing equality of opportunity as our goal, the moral frame is already given away. Equality of opportunity relies on the argument not being followed to it's conclusions, and these days it is pretty much guaranteed to be.
The better attack on this is that the analogy of the boxes is artificial. The universe of the problem is artificially narrow and quantifiable. It is the same narrow little trolley bus world in which utilitarianism, or libertarianism work just fine. A more realistic version would involve people who had no interest in watching the game being given boxes, elderly people who needed the box to sit on having the box taken away from them, while the cost of boxes is driven up creating scarcity in other places. Maybe people used to bring boxes to stand on, but they don't bother any more because they are just going to be taken and handed out to people who didn't. Now that free viewing is officially sanctioned, people stop paying for the seats and the whole things has to be subsidised. Maybe you can level the outcome of the visibility, but you have made other outcomes less equal to achieve that one equal outcome. If I worked for and paid for my three boxes, but you've taken two away and given them to people who did nothing for them, we've made one outcome equal, by making another less equal. It assumes an understanding of the problem, and an ability to fix the problem without creating worse problems elsewhere that is in question. Effectively the very things that are at issue are smuggled in.
The example of affirmative action seemed to be being referenced. It's been, what, 60 years? How is that going? I don't doubt that we know how to improve individual metrics.... one could after all just skew test scores, policing, or hiring practices along racial lines to hit particular targets. It won't be long before there are few people left alive who were around when we first started redistributing boxes. How much longer do we think will be required before we are done with this in, say, California? Not perfect, but good enough? 20 years? 100 years? Never? Do we actually know how to do what is depicted in the cartoon?
In theory yes - it's called communism. In practice, no, because the human animal isn't even vaguely altruistic enough to accept it.