He does pay for security, however Scotland Yard security is supposed to be the best and as a born royal, he has technically always been entitled to it.
Remember his mother gave up her security when she was divorced from Charles, obviously it was there when she was with her children but otherwise not.
To this day the people at Scotland Yard say had they been looking after Princess Diana, what happened would not have happened, for a start she wouldn't have got into that car and secondly there would have been a team of security which would have kept the harassing paparazzi away.
I don't think it is at all unreasonable for Harry to have the same security as the rest of his royal family if he visits the UK. It was an outrage that it was taken away so suddenly while he, Meghan and Archie were on Vancouver Island. Chaos descended. Thankfully they managed to escape and obtained some privacy thanks to Tyler Perry.
It's the principle as much as anything. As Harry himself says, he didn't ask to be born into the royal family but he was and therefore should be properly protected as they all are. I'm not saying it is completely foolproof, nothing ever is, but it is extremely efficient and round the clock.
I would like to see him, Meghan and the two children here sometimes. The two little ones are the King's grandchildren and the family needs to be able to relax, not worrying about people looking through their windows.