Yes, and some databases have REST APIs. In practice pure REST is usually blurred with RPC calls and optimisations (partial fetch, batch fetch). And the downside of the REST is that it’s not agile (you have to support both new and old clients explicitly), and manual: you have to write it manually for every endpoint. Good and efficient data fetch API for client-based rendering will very soon move very very far from REST.
In which direction do you mean? Also, I'm not sure what do you mean by "you have to write it manually", nor why do you have to support new and all clients explicitly. Care to elaborate?