It's a funny design/affordance. I do see them often writing memories of things that that feel unlikely to be important going foward / with other tasks, but I don't see them clearly getting tripped up by them as prior models used to. (eg: Since you're running Ubuntu in Canada, here are some drills you can try to help your kid hit a baseball more consistently.)
Yes, the mechanics are straightforward if Anthropic (or Claude, if you want to ascribe the decision there) decides to burn a pile of your money. But the strategy fails basic game-theory of repeated games - you'll simply stop playing.
(this isn't to say it invalidates the incentive to inflate token count, but it overcomes in terms of weighing options and making long-term profit decisions.)
In my enterprise-seated account I see slightly different options available (vs. my personal account) in the Capabilities section:
Search and reference chats
Allow Claude to search for relevant details in past chats.
Generate memory from chat history (Legacy)
Allow Claude to remember relevant context from your chats. Memory includes your entire chat history with Claude.
The first option was defaulted to on, if I recall.Claude code stores memory locally on the device, similar to how a developer stores notes.
Data retention is about storing your raw conversation data.
Capabilities and Privacy settings are used to manage memory and data retention.
When people talk about retention they mean API usage and terminal agents, which run on your device.