The person creating capital may not be someone who is liked, but they often produce jobs, and products/services that people want. Their capital comes about because of voluntary transactions within society. The so-called "social contract", meanwhile, is built on coercion.
I happen to believe (in agreement with you, I think) that private property rights look more useful (in a benefit-to-humanity way) than the rights that most people who use the term "social contract" think of, but I don't believe there's a clear philosophical difference between the two.
You can tell yourself whatever Rothbardian fables you like, but the only real business you're building without any participation in a modern, "coercive" society is a subsistence farm.
Corporations are indeed creatures of government. Are they required to conduct business? No, but they are awfully convenient, and allow for a lot of rotten things to occur.
Private property? If it requires government's nod, it isn't private. And, of course, we see this all the time, when government decides that it wants someone's property, and takes it. It might be your land, your automobile, or something else. It is all up for grabs.
Not sure why you're name-dropping Rothbard, but it doesn't help you here. No business is going to exist without participating in the existing society. Trade and commerce require cooperation. The alternative is what brings a society closer to subsistence farming (and it tends to leave people starving).
You can't escape your problems by pretending to define them away. No property regime has ever been secured without the use of government.
We've had a chance to see a number of government experiments run their course (some continue to), ranging from absolute monarchies, to Marxist-Leninists, to Maoists, to various kinds of republics. All of them have ended up going in similar directions, over time, consolidating power, though at different speeds.
Private property is just as coercive as taxation in the first place. You do not have a God-given right to make hundreds of thousands of dollars by investing millions of dollars and pay nothing towards the upkeep of society. Basic freaking social contract theory, and, in fact, basic law: financial instruments and corporations could not exist as they do except by government fiat.
Second, yes, he will make the sacrifice if everyone else does it. That's sensible. You don't solve large-scale systemic problems by individual action, not even mass individual action, but only by collective action. Again, this is just how the world works.