You can't buy a static IP that easily, you have to be assigned a block by one of the registries (such as RIPE in Europe). Single IPs are difficult to route and so you can't just say 'oh, I'd like that particular IP which no-one else is using' like you can with a domain name.

I have a static IP with my broadband connection, regardless of whether I'm online 24/7 or not, but if I change ISPs I lose it because it belongs to the group of IPs that are assigned to my ISP.