As civilians, they are responsible for their own security
Having left the Royal family, the couple is no longer classified as 'internationally protected persons'. It was this classification that meant state obligation to protect them. They now must live under the same expectations as every other private citizen.
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Royalty is the height of privilege. Royals are not only born into immense wealth, but also status, celebrity, and opportunity. Considering this, it is difficult to make the case that the Duke and Duchess deserve the state's assistance in their security. The fame and opportunities that they have been granted as a result of their public image guarantees that they have ample ability to provide the funding for their own security. Most importantly, they willfully dropped their royal duties, so they should expect to lose the benefits associated with their titles. Without their royal status, they are now just celebrities. The most powerful Hollywood celebrities pay their own security bills, so Harry and Meghan should expect to do the same. They made the decision to leave royalty, and they should expect to be responsible for their decision.
Despite making the voluntary decision to leave their royal titles behind, in reality, it is only in name. Harry and Meghan are still inseparable from their royal status, and still members of the royal family. Therefore, their security needs and risks have remained unchanged. The only thing that has changed is that they will no longer participate in royal duties, and will not directly receive public funds for their use. Their security costs may be inconvenient considering their departure from royal duties, but it is necessary considering that they still retain the public image that is impossible to leave behind.
[P1] Their decision to drop royal duties and titles means that they should lose all the privileges associated with their titles. [P2] The average celebrity pays for their own protection, so they should too.
Rejecting the premises
[Rejecting P1] They still have the status of royalty attached to their names, despite dropping their titles. [Rejecting P2] Their attachment to the royal family still means that they are vulnerable to safety concerns, and therefore the responsibility of the family and state.