I think you might find this line of inquiry more productive if you roll back on ethics, and don't give up either of "deserve" or "have" for free.
Start by tabooing "property" and assuming consequentialism. We have a monetary system that abstracts the idea of value; ownership isn't necessary for that to exist. The question we want to answer is, if we give an individual control over some value, and through their actions they cause additional value to come into being, how much of that additional value should we, through use of violence, enable them to control? The answer may range from "none of it" all the way up to "all of it".
Why would it be any of it? Possible reasons are at least twofold: First, that person may have demonstrated a unique ability to multiply value, which we wish to harness. Second, it may incentivize others who desire control to be more productive.
But lots more questions fall out of that. How likely is this person to be unusually productive again? How much of an incentive is this control to others, and how does it affect the overall growth of value? How much of an incentive is necessary to maintain our desired rate of growth? What is our desired rate of growth?
And on to more complicated ones: Say we decide to afford some amount of control. Should that amount be the same regardless of the value created? Should the scale be linear, quadratic, what? How should we respond to actors who fail to create, or actually destroy value?
As if that weren't enough to think about already, we now have to consider the externalities, what you might call "ethical" concerns. A couple of major ones:
Does our system unfairly determine the course of an individual's life based on the circumstances of their birth, making a mockery of the concept of freedom?
Does our system perversely incentivize us to manipulate it in order to increase nominal value, without an according improvement to the human condition?
This isn't intended to answer your question exactly, just to point out that 1) There are a lot of problems with the way we set all this up, but 2) We did set it up this way for good reasons, and 3) Anyone who takes all of this and gives you a "Of course they do" or "Of course they don't" has been indoctrinated.