If it was for just the free market to decide, we would never have gotten rid of child labor. The government also tries to ensure that its citizenry are lifted out of poverty etc., things that free market isn't really incentivized to care for. As the op said, "As a society, we've decided that certain offers aren't acceptable, even if you can find someone desperate enough to take the offer."
Am not sure if this situation with uber/lyft calls for this, but there definitely is a line that as a society we do not want to regress. Though, I do agree it is a very hard job to intervene because of unforeseen side effects, many times adverse, so if possible I would also prefer to avoid government intervention and let the market decide.
Free markets are excellent for lifting the baseline level of wealth among a nation's people (Marx admitted this as industrialization rapidly increased the wealth of Western Europe at the time of his coming of age). It does not solve the issue of wealth inequality, and exacerbates it to an extent to the point where an individual's wealth and the labor they expend to create that wealth are completely non-correlating -- you can work four times as hard as a laborer than an investor and not see any return while capital ends up with most of the value extracted from your labor.
Even the most pro-market economists acknowledge this critical, showstopping bug in the free market. Adam Smith acknowledges it. Friedman acknowledges it. Where opinions diverge is the solution, or whether the issue of inequality is even worth solving or worthy of government intervention. If you exit the toxic and obnoxious Silicon Valley Bay Area bubble, look out the window into an actual working class individual's life, I think you'll find plenty of evidence for that answer to be a resounding Yes.
The situation with Uber is similar, and California has decided that it is indeed worth the effort to allow drivers to keep more of the wealth they generate for the company. It's not communism, it's literally the first principle of commerce that individuals providing labor receive full compensation for their labor in return. There is no more a capitalist concept than that.
No; capitalism is a system based upon property rights and as such it requires that contracts are voluntary and mutually consensual. The USA doesn't have capitalism, it has a Mixed Economy, which combines aspects of capitalism and socialism.
In a relatively unregulated marketplace, an Uber driver comes with their time, equipment and skills, ready to trade them for money. Uber in exchange offers money and the use of its infrastructure and relationships. Together they potentially agree a price, but neither side, nor the government nor some other external entity can dictate terms of their agreement.
Wealth inequality is only an issue if your world-view demands that you makes it into one. In a free market, wealth inequality in itself does not affect a person's life in any tangible way. Your comment about the wages of laborers seems to relate to the Labor Theory of Value; this concept is often used in conjunction with a claim that labour is inabstractable in an attempt to dismiss the interchangeability of human labor for automation, but that's patently absurd, because we're talking about this on a messaging board for computer programmers. Our economic system, even with its burdensome and overweening regulation, still does a good job of allocating resources to productive enterprises and people, and I'm afraid that in the laborer-capital-investor example that you gave at the start, the worker is only gaining from the deployment of capital in proportion to what they themselves have deferred the consumption of and then risked in the deployment of capital (vice versa with the investor and their labor). And of course, that example is less applicable these days, because people generally have pensions and own shares.
(But don't worry, if I'm wrong, you can go ahead and make a ton of money proving it)
Am not sure if this situation with uber/lyft calls for this, but there definitely is a line that as a society we do not want to regress. Though, I do agree it is a very hard job to intervene because of unforeseen side effects, many times adverse, so if possible I would also prefer to avoid government intervention and let the market decide.