Recently, Stack Overflow posted a blog post about their Providence system (see also a 2015 blog post by Kevin Montrose about this same subject). This is related to the Personalized Prediction Data.
The Personalized Prediction Data tool lets me delete and stop collection of my personalized prediction data, but will hinder question suggestions. This means that I either allow Stack Exchange to gather large amounts of data and have access to tools that let me find interesting and relevant content or I disable it and don't. There should be a middle ground - identify a period of time, after which data is no longer relevant, and purge it.
We now have sites about the workplace, politics, various religions, health, and law. Consider a worse-case scenario - a person in a repressive regime viewing content deemed "bad" or that can be used to single them out for some kind of retribution. Actors, through legal or illegal means, should not be allowed to obtain data that can tie what types of content is viewed to an individual.
This isn't necessarily a far-fetched thought. Internet freedom is on the decline. In order to protect individuals, the amount of data collected, inferred, and stored by services (especially the data that can be tied to a particular individual) should be minimized while still maintaining the performance of the service. If the data is not collected or stored, it cannot (as easily) be obtained by third parties through legal (or illegal) action.