That's a part of Twelve Factor apps as well. No state in the app! And while there is a cost to keeping state in an external data store like Redis, there are costs to keeping state in the app as well. First, there is the question of complexity and testability. Your app becomes harder to reason about, harder to test, and much more likely to be dependent on complex integration to get to a testable state. Second, there's the need for external support for internal state in any horizontally scaled app. This can be very expensive.

Consider session state in a web app. If you keep state in memory and scale horizontally, you need session affinity, so stateless inbound http connections hit the same server instance. That means a session-aware router, delicate and extremely expensive F5s and other "smart" routers. But if the app is stateless and session state is in external storage, then all you need for load balancing is a simple round robin. A cheap router, that's more reliable and requires less administration, for a fraction of the cost.

There are other ways stateful apps are expensive, but that's a big one. I'd rather pay $5k than $100k for a router.