REST-API's then are especially suited for acting as a gateway to a database, to easily CRUD and fetch lists of information.
The best API's I've seen mix and match both patterns. RESTful API endpoints for data, "function call" endpoints for often-used actions like voting, bulk actions and other things that the client needs to be able to do, but you want the API to be in control of how it is applied.
I don't disagree, but I've found (delivering LoB applications) that they are not homogenous: The way REST is implemented, right now, makes it not especially suitable for acting as a gateway to a database.
When you're free of constraints (i.e. greenfield application) you can do better (ITO reliability, product feature velocity, etc) by not using a tree exchange form (XML or JSON).
Because then it's not just a gateway to a database, it's an ill-specified, crippled, slow, unreliable and ad-hoc ORM: it tries to map trees (objects) to tables (relations) and vice versa, with predictably poor results.