I already addressed size in the original post.
If homesteading just allowed you to claim the product of your labor, you would have a point. But it does so much more than that. It gives you the product of all future labor done on that site, and it allows you to leech off of the production of the surrounding community. According to that principle, building a mine should give you the right to claim only the ore you dig up, and not the ore that's still in the vein. Yet, taking the vein as private property allows you to do both.
No, by digging the mine, you alter the land. You thereby gain ownership of the
land. The ore, both in the vein and dug up, is part of that land
As I pointed out in the last thread, the first person could "homestead" one year, and then the next person to arrive could spend the rest of their life doing the exact same work on the exact same land, and the first person would get most of the reward. Why? Just because he got there first?
Care to explain how the first person gets most of the reward? Even if he rents it, He won't be able to charge more than the renter is willing to pay, and if the area is rich in ore, prospective renters may value that already dug hole less than the money he's charging for it, and go stake their own claim.
And, there's no clear line regarding how much land a given act of homesteading entitles you to. In the last thread you gave the example of breaking a trail to claim a section of wilderness. How much wilderness does a trail entitle you to? While it sounds nice on paper, I really think homesteading is too arbitrary to base a system of property rights on.
So drawing a line on a map is less arbitrary? hmm, no. And your system has the same problem. How much land do you charge him for, if he breaks a trail trough the woods? All the woods he's thus altered? (ask FirstAscent exactly how) Just the trail? some area (line of sight?) around the trail?
Besides, how would you even go from the current system, where property consists of lines on a map, to a homestead system? A number of people own land without marking it, would that revert to the commons after the revolution? A number of people own land that is marked or occupied, but did not earn it justly, what happens to them?
You're aware that most land in the US
was homesteaded? And I've explained a transition like this before. Gov't land is up for grabs, with the current users of it getting first "dibs" (the President would get some sweet digs), Private land, unless clearly stolen is assumed to be legitimately gained. Do some people get screwed? Maybe. But a lot fewer than the current system, and fewer than yours, too.
Also, why do you care how the government claims sovereignty over land? In your words, you never had it, so it was not taken from you, so why worry about it?
Well, I never had my neighbor's yard, but I did legitimately gain my house. I do have it. Their claim conflicts with mine. That's why I care.