Indeed, my understanding with the policing of football games, concerts etc is that the police operate as they see fit and necessary to keep public order and keep people safe. The organisers then reimburse some of that cost so it is costing the taxpayer less. However, what the concert organiser or football club can't do is say - "oh no we want 100 officers there not 50, but don't worry we'll pay for it"
This is essentially what Harry is doing - I'll pay but only if I get armed protection to the level I want" Is he, I wonder, reimbursing the costs of the protection he does receive from the police when he is the UK, as he is receiving some, or is the offer to pay only when he gets the level of protection he deems necessary?
The difference to most is clear - for football games, concerts etc the police have a duty to act and protect those attending, so they are left to work out what operation and level of support they provide and left to get on with it, the organisers then reimburse some of that cost out of their potential profits to minimise the cost to taxpayers.
What Harry is asking for is a pay for a level of protection the police and security service do not deem he needs. That is different.
If Harry wants to be treated like the football clubs are, he would allow the police to protect him at the level and in whatever way they deem necessary and then repay some of that cost.