You can swap the word "capitalism" in for "socialism" in your comment, and those statements would still work. Socialism didn't fail because it were monstrous. It failed, because we ran out of money and the will to live in squalor.
The word "free" in free market capitalism means freedom from political coercion or force.
The CEO owns the company. If he has total control, he could instead of paying his workers more simply buy himself a jet or donate it to a church. (Obviously, if his shareholders object, he'll have to convince them to go along as well). If you want to think in terms of market wage, what he is doing is paying them market wage, then unilaterally deciding to give them a "big tip" at his own expense - which happens to bring their total compensation to $70K a year. That's still capitalist, since it was his money to give away in the first place. He could give it all to Donald Trump instead, if he wanted to - the fact that he happened to give it to his employees is almost arbitrary. The only issue is whether he can afford to keep it up, but that's entirely on him.
Your example is talking about one housekeeper: if she notices that she can arbitrage on your generosity, she can pretty much contract someone else to do her job for $10/hour, and not even show up and still earn $10/hour. If you object to it, it is a signal that you value one's work more than the other, and then we are not talking about market-clearing prices anymore, are we?
In the end, the only way to end this and to actually get your house cleaned is to pay market-level wages.
Or to train people to do as well as you and set up your own business taking advantage of your stronger than average reputation in the field.
But doing an activity which has a high probability of costing you the income you desire is not rational.
Let's suppose the market wage is $10/hr. If I offer a lucky housekeeper $20/hr, why wouldn't she just happily take the money and continue to work? Union workers don't arbitrage themselves (but they should, under your scheme, because they collectively bargain for higher than market wage).
If the cost of deceiving me is greater than zero, then she's being irrational. She can earn no more than $10/hr anywhere else, and hiring someone else to replace her would cost $10/hr (since that's the market rate). So lets say she hires someone else at a cost of $10/hr, and then goes to work for someone else - she's still earning $20/hr (the arbitrage amount plus the value of her labor) minus the cost of deceiving me. So assuming she wants to work for wages (which she must, since she offered to work for $10/hr in the first place) I don't see how it's at all rational to arbitrage the opportunity.
I bring someone else to work with me, and we both do the job in X/2 time. I pay $10/hour for the subcontracted person.
So assume a 8 man-hour job. You will pay $160. I keep $120, the subcontracted $40. My effective rate was $30/hour. You don't think this is a problem, as you see your house cleaned just like usual.
Next time, I bring 3 other people. We finish things in 2 hours. I pay $60 to them, I keep $100. My effective rate was $50/hour.
Next time, I bring 7 other people. We finish things in one hour. I pay $70 to them, I keep $90. My effective rate was $90/hour. I use the other 7 "working" hours of the day to play videogames.
How are you able to assume this, since I actually would very much see it as a problem if 3-4 people I don't trust to clean my house as much as my housekeeper are inside doing the job? Your underlying assumption is that I'm an idiot and can't see what's happening. She couldn't subcontract the work for the same reason I can't subcontract my work at my current job - my employer would see through it.
> I use the other 7 "working" hours of the day to play videogames.
Not many people would come out for $10/hr for only one hour. What about travel time? And the organization necessary to make sure the quality is still high? I think you're lampshading a ton here.
But actually I think you're on to something - basically Dan Price is saying he thinks the true market value of the labor provided by his workers is actually $70K a year. And what I'm really saying with my housekeeper is that I like her so much that in order to prevent any risk of her defecting to another employer I'm willing to pay $20/hr instead of $10/hr. She can try to arbitrage, but that means working for someone else for $10/hr, but since I assume she actually wants to work, why would she work for anyone other than the person who values her work the highest? So we're still in capitalist land.