This architecture is roughly how HashiCorp's Nomad, Consul, and Vault are built (I'm one of the maintainers of Nomad). While it's definitely a "weird" architecture, the developer experience is really nice once you get the hang of it.
The in-memory state can be whatever you want, which means you can build up your own application-specific indexing and querying functions. You could just use sqlite with :memory: for the Raft FSM, but if you can build/find an in-memory transaction store (we use our own go-memdb), then reading from the state is just function calls. Protecting yourself from stale reads or write skew is trivial; every object you write has a Raft index so you can write APIs like "query a follower for object foo and wait till it's at least at index 123". It sweeps away a lot of "magic" that normally you'd shove into a RDBMS or other external store.
That being said, I'd be hesitant to pick this kind of architecture for a new startup outside of the "infrastructure" space... you are effectively building your own database here though. You need to pick (or write) good primitives for things like your inter-node RPC, on-disk persistence, in-memory transactional state store, etc. Upgrades are especially challenging, because the new code can try to write entities to the Raft log that nodes still on the previous version don't understand (or worse, misunderstand because the way they're handled has changed!). There's no free lunch.