I'm thinking that you just need one website where you can associate a given fingerprint to a specific user and then tracking its activity around the web becomes easy.

Let's say I'm logged in a famous search engine, they associate my fingerprint X to my account A. If they then encounter fingerprint X anywhere else, there is a good chance it was me, A, doing it. If the next day I get fingerprint Y, it gets attached to A as well and the tracking information follows it.

Does this make sense?

You mean, like a really popular web service or app that someone would log into every day/week/month...?

Even easier if, additionally, many of the smaller websites were syndicated into a tracking network?