It not being a zero sum game doesn't make it a win-win game (or whatever the true opposite of a zero-sum-game is, I had to google to even get to win-win game.)
A wage gap alone is not a problem. The wage gap in the current US system that makes the rich richer and the poor poorer in a country where almost 40 million people are living below the poverty limit is a problem. Coming back to my earlier points about education, food security and health care the importance of this on a societal level seem self evident to me. When the system is creating more poor people, whilst making the rich richer the wage gap is not only symbolic or related to expectations.
Those at the bottom do not have enough. So the wage gap is relevant. The current system is making more of those that don't have enough whilst those at the top keep getting richer, and again the middle class is also shrinking. This system is not working as it should, and the wage gap is a quick way to talk about those flaws.
I imagine your issues with the wage cap conversation is more philosophical than practically related to the current US economy?
No, they're practical.
If you increase wages then you just increase inflation - everything costs a bit more and people are (eventually) back where they started. So you have to increase wages again to compensate for inflation, etc etc.
In a global market, your workforce then becomes thoroughly uncompetitive. The people who cannot do much more than flip burgers (and there's no level of education that will improve that - trust me, I've employed plenty of them) are now getting paid a few times more than more highly trained staff in the countries with which you compete for trade, your international sales dip and so now there's only an internal market for your products. This is likely to end up in a contraction of the market, as industries used to selling all over the world can now only sell in the US. You start to lose the supporting industries and jobs with them.
At this point the market is likely to do one of two things, have a race to the bottom for prices in an attempt to keep a large share of what little market is left or increase prices because of the scarcity of the products being produced. If the market tanks then we can't afford to pay the silly wages, if it bumps then we have to increase wages even more to account for the rising cost of living. Any sensible investment from this point will be in plant & machinery, not staff as even the lowest paid staff will be prohibitively expensive to employ.
All systems have flaws, all systems (in the real world) will leave people with less than they ought to have. At least a system where the government keeps out of the way wherever possible has a chance of being efficient, a chance of being even handed and a chance of giving people the freedom of choice that we all naturally crave.
How much value do you place on their children who are at a much higher risk for a whole host of very costly outcomes for society? And have a much lower probability of fulfilling their promise or talent of becoming one of those people you and market forces value much higher - at least on a societal level...
Again this comes back to my earlier points. To me logical conclusions from your arguments is strong nepotism and a class system. I think I can make a decent moral argument against that based on humanist ideas, but just as interesting and important are the economic costs to a society.
There's certainly nothing wrong with a class system - it creates a very strong force of ambition with even bigger prizes for those that succeed.
Regarding the next generation, I'm conflicted. As I'm sure you've gathered, I don't believe the government should have any right to meddle in my business. I'm an adult, I'm perfectly capable of making my own choices and I also (believe it or not) want to do my bit for those that require it. That said, some of the children that turn up at my wife's school make me wish there was an enforceable parenting license.
In the UK, even with the class system that still exists as a barrier in most people's eyes, it's entirely possible to go from a barely surviving working class family to a very comfortable middle class one in a single generation. Within my family and (close) friends I could show you at least 4 or 5 cases of this. So I don't see any evidence at all that those without cannot achieve, or that they cannot change their lot in life in a society that leans a lot further to the right than Sanders does. Is it difficult? Yes, of course - but I don't see why things with great reward should be easy.