Explanation
Cloudflare's service still runs on real hardware that can only process so many requests per second, so depending on the amount of traffic a single datacenter is getting, CF may choose to route visitors to datacenters farther away to alleviate the load of the DC so that it can provide high-quality service to its highest-paying customers.
See this graphic from page 79 of the Cloudflare S-1:
See "Network Prioritization" - Lower-tier websites will still work if they don't pay, but the latency might be higher for some visitors if their closest datacenter is experiencing high load and CF has to divert traffic.
Cloudflare's direct reason from their S-1:
Free customer base—Free customers are an important part of our business. These customers sign up for our service through our self-serve portal and are typically individual developers, early stage startups, hobbyists, and other users. Our free customers create scale, serve as efficient brand marketing, and help us attract developers, customers, and potential employees. These free customers expose us to diverse traffic, threats, and problems, often allowing us to see potential security, performance, and reliability issues at the earliest stage. This knowledge allows us to improve our products and deliver more effective solutions to our paid customers. In addition, the added scale and diversity of this traffic makes us valuable to a diverse set of global ISPs, improving the breadth and economic terms of our interconnections, bandwidth costs, and co-location expenses. Finally, the enthusiastic engagement of our free customer base represents a “virtual quality assurance” function that allows us to maintain a high rate of product innovation, while ensuring products are extensively tested in real world environments before they are deployed to enterprise customers.
Anecdotally, only once every few months for the Atlanta area; but I suspect that's a high-cost and highly-provisioned datacenter due to the amount of people it generally has to service.
There are many datacenters, and some are smaller than others, so depending on your location it might happen very often. Generally, enterprise sites will always get the closest DC unless the DC is rerouted.