No. Other forms of property can a) be manufactured and b) be moved. Land is unique in that both are impossible. As result, each piece of land is unique because of what it's close to (not what it is, as with other forms of property). That means that if you want an alternative equivalent product from another supplier, it's impossible. All the other bits of land are in different locations, and you can't get a new bit from a factory.
This means that if you want to a) live walking distance from your parents (free childcare, so your partner can work and you get double income) and b) be able to commute to your place of work, there are certain number of qualifying pieces of land and no more. If someone already owns them all, you have no other choice but to buy or rent one of those. No entrepreneur can undercut high land prices with a cheaper equivalent, therefore it's a monopoly.
Land is different in many important ways, but this does not make it a monopoly; you do your cause a disservice to co-opt that language. Something doesn't fail to be a market just because it's not a commodity (where the things being bought and sold are identical/interchangeable). The art market is a market even if there is only one Guernica.
Yes, of course, in the limit where there is particular item for which there is no substitutes, this approaches a monopoly. Hence, certain pieces of land can roughly be described as monopolies, as can, say, the Mona Lisa. But this doesn't make it reasonable to characterize most land as a monopoly. Most land is substitutable, for most purposes and for most buyers, by different land. The unrealistic supposition that "someone already owns them all" in your hypothetical highlights this. How often can anyone say "I rented a house/apartment for which there were zero feasible alternatives from another seller"? Almost never.
A monopoly doesn't mean there are no alternatives. It means that the process of competitive undercutting of prices does not operate. Consider a price fixing cartel. There are alternative products, but it is still a monopoly.
I didn't explain the example I used very well. In the case you mention: renting an apartment, there are indeed always alternative locations. However, that does not mean the market is competitive. The key difference is that from your perspective, these bits of land are equivalent, but from other people's perspective, they are not. One of those locations that you may consider to be nothing special may be another person's number one choice because it's close to something they value, which you don't care about. That could be friends, family, work, amenities, businesses that your business depends on, raw materials, transport links, etc, etc. Each buyer has unique needs and each location has a unique set of things it's close to. That means that the seller/landlord does not need to bother attempting to attract your business in a competitive way as this other person for whom that location is their best option (and likely others too) will already have approached them. In effect, each unique location is an auction, with a different group of buyers interested (at different prices) each time. This only happens because land doesn't move. If it did move, then the locations would not be unique and the market would work more as you imply it would.
The outcome is that each piece of land is sold based on the highest bid offered by any buyer. A characteristic of a monopoly. This is the opposite of a free market, where things are sold as a result of the lowest price offered by any seller.
I'm happy to agree that "all sellers in a market perfectly coordinate on price" is functionally equivalent to "there is only one seller in the market", and that this qualifies as a monopoly. My comment doesn't hinge on that obvious point. (Indeed I said "alternatives from another seller", not just "alternatives", and it's pretty clear that nothing changes if all the sellers perfectly coordinate as one.)
Your explanation doesn't save your example. It will always be the case that, for any given buyer in a non-commodity market, one choice is better than all the other. (If the products are not identical, one will essentially always be at least a bit better than the others for some reason.) However, this doesn't approach a monopoly except as the alternatives become arbitrarily bad in comparison (i.e., do not function as substitutes). Yes, in this limit, it's a monopoly, but this is almost never the case.
Your remaining comments imply that anything sold at auction is a monopoly and not a free market. You also incorrectly ascribe this to lack of mobility:
> In effect, each unique location is an auction, with a different group of buyers interested (at different prices) each time. This only happens because land doesn't move.
Art, used cars, items on eBay, etc., are all products that move (unlike land) yet "each...is an auction, with a different group of buyers interested (at different prices) each time".
Again: the key mistake is that you are conflating all non-commodities as monopolies.
Hardly. Others can still fly over it. Look at it. Zone-regulate the use of it. Enforce environmental regulations on it. Pursue criminals over it. The nation can assert hegemony over it.
Ownership is a limited-use social contract. There's less you can do every day.
I like this definition: "There are two types of ethically invalid land titles: "feudalism," in which there is continuing aggression by titleholders of land against peasants engaged in transforming the soil; and land-engrossing, where arbitrary claims to virgin land are used to keep first-transformers out of that land. We may call both of these aggressions "land monopoly"—not in the sense that some one person or group owns all the land in society, but in the sense that arbitrary privileges to land ownership are asserted in both cases, clashing with the libertarian rule of non-ownership of land except by actual transformers, their heirs, and their assigns." — Murray N. Rothbard, The Ethics of Liberty
Land redistribution is a difficult idea to sell since it means the use of force to do it. And when you think that all lands, now legal, have been taken by force, or chance at some point in the past, how do we deal it?
Think about it: Even your perfectly legal little house, was taken by force or chance at some point back in history.
