Cookies do empower sites a little more. Cookies don't share, but they are not that secure either. Sites normally don't share cookies, so there isn't a way for site X to know about what you do on site Y. Site X could cheat, and try to read site Y's cookie, but to my knowledge, no one wastes the energy to snoop other people's cookies. And even if they could figure it out, the other site can change the format to confound the unauthorized snoopers. Each site would have to know about every other site's cookies to be of much value, so it isn't worth the work.
Cookies come in secure and insecure varieties.
Most sites use the latter, and because they know the cookies are not secure, they don't put anything of interest in them. The cookie is just to identify the relationship to you, so the site can bring it up on demand. But if they have a receipt by itself, it probably doesn't mean much. Instead they require you to log-in and enter a password to help you guarantee your privacy. This way, neither your kid, your live-in flaky relative nor some snooper on the net, can buy things in your name.