Another easy analogy would be IP addresses. Early on in the internet huge chunks were just given out for free. Now they're valuable because they're scarce and the demand for them has skyrocketed as the internet grew.
You need spectrum to participate in the radio business (and other kinds of businesses). You need IP addresses to participate in the internet. Similarly you need HNS (as an example) to participate in the Handshake network.
And as with spectrum and IP addresses, there's only a fixed amount of HNS (or at least that is the expectation, the details vary in each cryptocurrency).
The reason that IP addresses are scarce is not because it's not possible to invent a new protocol, but because everyone else uses IP so only IP addresses are useful.
Spectrum might initially appear to be fundamentally scarce, but even then, people can invent other ways to communicate (and they did! copper wires! IP!).
These are all examples of networks - their value is proportional to their popularity. So yes, anybody can create a new cryptocurrency, but currencies are mainly valuable because of who you can use them with. Dollars are valuable because so many people accept them!
So if one cryptocurrency really gains traction, it will be hard for any other cryptocurrency to compete unless it offers something fundamentally new and different.
Yet the vast majority will still use .com, .net and .org, and those still remain the most valuable. :)
So something analogous to owning a part of the network, would it be correct to say that, for instance, governments own and auction telecom spectrums to businesses. They do make money out of that ownership through the initial auction price and then potentially tax you later. So a cryptocurrency could be looked at in a similar way in the future. When you later sell the currency you have owned for a while (given that it takes off well over the couple of years), you are basically transferring that "spectrum" ownership to another party.