This design makes it easy to implement optimistic updates, rollback, replays, automated testing, and recovery after a disconnection. It's a surprisingly good fit for UI, too; you can render simple games as a React component which takes the current State as one of its props.
However, a stream of context-free actions can be a really inconvenient representation for some games. The rules of a board game are often like the control flow of a computer program: you'll see branching, iteration, local variables, function calls, structured concurrency, and sometimes even race conditions and reentrancy. When you try to represent all of this logic as a State object, you're basically maintaining a snapshot of a "call stack" as plain data, and manually resuming that "program" whenever you handle an action. It doesn't seem ideal.
I've been sketching a board game engine which would represent the game logic as normal code instead. It seems promising, but it really needs a couple of language features which don't exist in the mainstream yet, like serialisation of suspended async functions.