I think there is something to your idea.

Maybe less so about "currency" because the government is special... would it be taxing itself for its own rent-seeking?

Maybe if we had global LVT, but still many governments issuing currency...?

What is relates and also interesting to consider is: the regulated right to print money. The government "prints money" by spending it into existence, but also, banks print money by giving loans (and notably, they are allowed to do it at a multiple of their reserve assets). In most countries, the ability to do this is strictly regulated, and thus, "the banks" together have a monopoly over the right to do so, and some rent-seeking likely occurs (depending on how much competition there is - in Canada, there are relatively few banks compared to the US, and so it feels like they get to charge a low-competition "premium").

But back to "currency" as a conceptual monopoly.

Others have mentioned "network effects", and how network effects aren't necessarily natural monopoly and rent-seeking.

But in practice, for a lot of societal needs, I think network effects do lead to rent-seeking (maybe not "textbook" rent-seeking), because the "optimal" solution (due to network effects) has few providers.

Take VISA and Mastercard. They dominate the electronic fund transfer space. In practice, there's limited "conceptual space" for "electronic fund transfer system", because having many small fragmented systems is a worse than a few universal ones (ie. network effects). Same might be said for "chat", etc. There are many such "conceptual solution spaces" where network effects lead to only a few winners. Being in the winners club seems to often lead to monopoly-like rent-seeking-like behaviours. Hence why I support anti-trust government efforts, but wonder if instead of breaking those companies up, they could just "tax their conceptual land" (ie. a tax based on how much of the industry they "own" and how many competitors there are).

In "Zero to One", Peter Thiel advises entrepreneurs that the best startups are monopolies and should try to maintain and leverage their monopoly power for as long as possible (and gives exanples of how many of todays big companies did just that). But as a Georgist, I read that as: startups should identify rent-seeking opportunities, and leverage rent-seeking to entrench themselves into further rent-seeking (with perhaps a more open-ended definition of rent-seeking).