This is a shared burden
We cannot hold the royal family to the same expectations as the general public. Harry and Meghan have a burden that is partially the state's responsibility, but their decision to drop royal duties means that they should pick up some of the costs.
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The royals exist in a context much unlike most public figures. One part celebrity and one part governmental figure, they can't be expected to live by the same expectations of either party. If they were simply celebrities, then they would not have threats from terrorist organizations, as Princes William and Harry both received during their military service. If they were only figures of government, they would not receive the sensationalism and celebrity that they often do. Most importantly, they had no choice in their birth into royalty, nor do those who marry into it have a choice in who they ultimately love. With this in mind, the Duke and Duchess's decision to forgo their royal duties, in favor of a more independent lifestyle should also be reflected in their royal privileges. They are still subject to the dangers that figures in government are often threatened by, but much of their attention is merely paparazzi and media. They should be willing to acknowledge this mixture of exposure that they are subject to, and realize that the state cannot be solely responsible for their safety.
The royals may seem like official figures in government, but they are nothing more than celebrities. The media attention and celebrity that they receive—particularly the lives Princes Harry and William—are indisputable evidence of this. They hold virtually no state power, and therefore should not benefit from disproportionate funding from the state. In Harry and Meghan's case, they should think of their royal duties as a job with benefits. If they no longer want to perform their jobs, then they should have no expectation of receiving the benefits that come with it. Plus, they will be able to make millions from their popularity, with or without royal titles.
[P1] The royal family exists in a different context, and therefore cannot be held to the same expectations of autonomy. [P2] The couples' decision to leave behind their royal duties means that they should also expect to leave behind some royal privileges.
Rejecting the premises
[Rejecting P1] The royals are nothing more than celebrities with official titles. They should be held to the same expectations as everyone else. [Rejecting P2] You can't leave a job and still expect to be paid. They don't deserve any of the state's help.