If the website you're ultimately visiting can see your IP address anyways, I fail to see the lost privacy. Their traffic will be sliced and diced into cohorts a

If the website you're ultimately visiting can see your IP address anyways, I fail to see the lost privacy. Their traffic will be sliced and diced into cohorts along many axes, and this is only one axis on which you are slightly anomalous. If anything, you'll be targeted less as a result since you won't show up in their funnels.