Rents by the OP's definition are the kind of revenue sources you wouldn't have in near-statelessness, which means it takes state bias to create them. Without a state it would be hard to lay claim to vast swathes of land peacefully, and homesteading would be abundant on unused land. Even in a simplified state model that offers courts to protect property rights with, you couldn't have the widespread real estate market manipulation we can simply observe with how out of control land prices have risen in the past twenty years.
And that's not even getting into bailouts.
Technically to consider it a rent the copyright holder would not be producing anything, which just isn't true. Well, not for patents on genuine inventions.
The same is true for financial services. They do provide a service for the money.
Even by the (overly restrictive, IMO, as it excludes economic monopoly rents that are not derived from government-granted monopolies), copyright and patent are sources of rents drawn on the government-issued monopoly right to exclude others from duplicating the covered subject matter (or, in the case of patent, even independently developing it).
Even that restrictive definition upthread does not included the requirement that the rent-seeker was not required to produce something in order to secure the government-granted privilege from which it extracts rents.