The event store and the cache are both part of the same system, and it's this whole system that is "eventually consistent".

Say I create widgets on screen 1 and they are persisted with event sourcing into Postgres. I see the list of created widgets on screen 2, loaded from a materialised view in Postgres (or Elasticsearch). The "lag" between it being created on screen 1 and appearing on screen 2 is the "eventual consistency" issue I'm referring to here, whereas I think you're referring to the consistency only of the persistence on screen 1.

I'm sure we both agree there's no getting away from CAP theorem. Event sourcing accepts less consistency, and every part of the system needs to deal with that.