Things are different in third-world countries, but at least in the US, the rich person with 24/7 security is a rare beast. Go look for yourself and drive through some wealthy neighborhoods. They have alarm systems like us plebians, not bodyguards.

There are certainly exceptions, for the super-rich and some kinds of celebrities, but it's not very common.

Well, if we are including all millionaires, I doubt the majority of them have a security detail, as that would eat into a million fairly quickly unless you underpay them, in which case you are probably increasing your risk.