My understanding, and it may well be incorrect, differs slightly.
Paying for the security, and the level required, wasn't the issue. What he was asking for was his security team to be given access to intelligence information available to those tasked with royal security, but not available to a standard rich visitor.
Quite why he believes he should still have access to some of the privileges of royalty despite having very publicly stepped away from the role isn't clear.
I feel some sympathy for him, and I'm not a monarchist. He didn't choose his parents, and he didn't enjoy his life.
Having chosen a different life though, that's where my sympathy evaporates. He's chosen to be an ordinary millionaire, and the press interest he claims to despise is his main income opportunity.
He comes across as just another rich person who wants everything on their terms.