Different people can use different equipment. Even in this oversimplified example, a person who's never touched a backhoe is not going to use it effectively compared to someone with training. Capability variance can get much larger than that.
The failure in interacting with this example was not mine.
Let's go back to the example.
People who can use shovels > people who can use backhoes. True for other tech too. You're also dodging the reality of productivity variance between these workers.
We were discussing how it's possible to measure individual productivity. Your example doesn't compare the productivity of two different workers, it compares the productivity of workers
along with the technology they're using. Unless you can figure out a way to actually separate the contribution of a worker from the contribution of the tools that worker uses, then that comparison is meaningless if your goal is to isolate the individual contributions of people. Of course, since such a separation is an impossible task, it quickly becomes apparent that the theory itself, and the whole idea that individual productivity can be objectively assessed, is meaningless. It's a circular reasoning, ultimately invoking the thing it's supposedly explaining as its own explanation.
Why are people paid what they're paid?
Because that's what they contribute to the economy.
How do we know how much people contribute to the economy?
Easy, we just look at how much they get paid...oh wait...
Even reckoning without the fatal problems with the theory that I have already explained, the theory only holds as long as the standard bourgeois economics assumptions of perfect competition, perfect information, and so on hold. Which they don't, ever.
I don't want to live in a society where people can take stuff from each other on a whim (by force or otherwise) with no consequences beyond the retaliation of the party losing it. It seems most societies of people feel similarly, and so create/enforce property rights.
On one level this is a wholly unobjectionable explanation of why property rights exist. On another, though, this framing of property rights hides some very important questions and issues. First of all of course there is not one system of property rights. The clearest example I can think of for this concept is that the US had a very different property system prior to the abolition of slavery, than it had after the abolition of slavery. Of course, the property system as whole is constituted by a vast, unimaginably complex system of rules, including civil law, case law, the common practices of property owners, and so on. So every little change to any law or rule relating to property ownership represents a "different" property system in this sense. But it seems rather absurd to characterize a property system that includes a property right to slaves in the way you've done, doesn't it? Slavery seems to be the
exact definition of "a society where people can take stuff from each other on a whim (by force or otherwise) with no consequences beyond the retaliation of the party losing it."
Of course, this is obviously not some sort of mere footnote as historically slavery has been hugely important in many property systems. In the antebellum US slaves were by far the most valuable capital asset; Roman property law also dealt heavily with slavery as is evident from surviving records of court cases and legal rulings.
What I'm getting at here is that while you have explained the widely-agreed purpose of property systems pretty well, you have elided the issue that there are property systems that are better and worse at realizing those ideals. And while the property system we have now is pretty good, certainly better than most that have existed in history, it is not really fulfilling its purpose. It isn't guaranteeing fairness, and we currently live in a society where "people an take stuff from each other on a whim with no consequences beyond the retaliation of the party using it."
So for example, we have drastically different standards for the sorts of things that people can claim a property right over. The TPP had provisions that allowed corporations to claim a property right to future profits, and to sue national governments for passing laws that interfered with these future profits. But if a worker tried to sue a corporation for cutting pay, claiming a property right to their future wages, the case would almost certainly be laughed out of court. One of the most egregious examples is our system's total failure to deal with the challenges posed by global warming. As the developed world burns through the world's carbon buffer, we are destroying the property of people mostly in the global south who live near the ocean. Entire island nations, with all their property that cannot be moved, are going to be swallowed up! What institutions or fora exist for these people to make their property claims against the carbon-burners? Another example; the Brazillian government has granted property rights to vast tracts of forest to (often foreign) extraction (mining, logging, oil drilling, etc) corporations; the property rights of the indigenous tribes who have been living in these forests for millennia go ignored.
And the world is full of injustices like this, full of totally inconsistent applications of the principles supposedly underlying property rights. This is why Adam Smith observed all the way back in the 18th century that
civil government, so far as it is instituted for the security of property, is in reality instituted for the defense of the rich against the poor, or of those who have some property against those who have none at all.
You notice he made the same mistake, of sweeping all the variation between different property systems under the rug. It's perfectly possible to imagine property systems that would tilt the balance of power decisively against the rich. For example, if we recognized the property rights of workers to the products of their labor, rather than handing those rights over to the owners of capital. Or the property rights of Bangladeshi peasants in their land when those lands are made useless and submerged beneath the sea by the actions of people halfway across the world. Incidentally, this is a beef I have with Marxists who take for granted the bourgeois/ruling class assumptions about property that make existing property systems unjust, and rather than saying "let's change the way this works so that it works for all the people instead of just the rich" they take the (much less productive) path of saying "Let's get rid of this entirely!"