I think the two are inextricably linked. Natural rights define who we are as humans in a political sense, and government is created to defend those rights as a primary function. That's why we value things like the common defense, a court system to settle disputes, etc. We don't kneel before them as the creator of our property rights, as those things already exist without the advent of government.
It's not about kneeling, and there's no "them." And, no, property rights don't exist without gov't. I've used the example of enclosures before (and
@Limbo Pete could add to this, using some earlier examples). You have peasants farming on common land, and the gov't closes it off and gives or sells it to individuals. Now the peasants have no way to survive except by working for someone who owns property (and helping that along, vagrancy is made a crime-- punishable by death in some cases). That's how we get wage workers (and the Industrial Revolution) and property. The mechanisms aren't always the same, but something like that is where property comes from. You bring up Locke in support of your own position, but he recognized the issue:
Nor was this appropriation of any parcel of land, by improving it, any prejudice to any other man, since there was still enough and as good left, and more than the yet unprovided could use. So that, in effect, there was never the less left for others because of his enclosure for himself. For he that leaves as much as another can make use of, does as good as take nothing at all. Nobody could think himself injured by the drinking of another man, though he took a good draught, who had a whole river of the same water left him to quench his thirst. And the case of land and water, where there is enough of both, is perfectly the same.
Basically, as long as others have access to land of equal value, there's no issue with enclosing some of it. But in modern societies, it's all enclosed. That is a gov't-imposed restriction on the freedom of people. On the other hand, the system that enclosures led to produced great wealth continues to. So we don't necessarily want to go back. But it's small consolation to the masses if the system (that entails forcibly keeping them from using land) produces great wealth that doesn't benefit them. The only moral solutions from that perspective are either stop maintaining property rights or redistribute the benefits of the system. And the first of those, while morally defensible, is terrible from a practical standpoint.
I absolutely believe in the lawful transference of property rights, which is what income is at a fundamental level. I help you build a house, and you compensate me with a good or service that I agree upon. A common currency merely assists us in equating value along a common standard and gives us an outlet other than an equivalent good or service. If I help you build a home, I don't want to be paid in 800,000 apples, haha. But in exchange for assisting you with your property, you can pay me in dollars, which I now own. As someone who is free to do what I want with those dollars, I can invest them. And all investing is, at a fundamental level, is buying ownership in a stake of a business in exchange for the business having my money to expand the business.
Note that "ownership" of a business in that sense is a gov't-granted ability to take the product of the labor of others. As with land ownership, it can be defended on the grounds that it leads to more wealth creation, but that defense only matters if the benefits of that additional wealth creation are broadly enjoyed.
It's become a little more complicated with the advent of brokerage firms, but the principle remains unchanged. So how is that like any other form of income? It's all fundamentally how we decide to utilize and risk our own property? The input of labor isn't really relevant to the conversation, IMO.
If you don't value human freedom, then, yes, labor is irrelevant. Just an "input" into a mechanical process that deserves no more consideration than a rock. But if you see human well-being (with freedom an essential part of that) as the object of policy, labor (the activity of humans) is fundamentally different.