When learning Scala, one of the first things I learned was that every function returns something. There is no "void"-function/method as there is, for instance in Java. Thus many Scala-functions are true functions, in a mathematic way, and objects can remain largely stateless.
Now I learned that the actor model is a very popular model among functional languages like Scala. However, actors promote a fire-and-forget style of programming, and callers usually don't expect callees to directly reply to messages (except when using the "ask"/"?"-method). Therefore, actors need to remember some sort of state.
Am I right assuming that the actor model is more like a trade-off between scalability and maintainability (due to its statefulness), and could sometimes even be considered an anti-pattern?
Yes you're essentially right (I'm not quite sure what you have in mind when you say scalability vs maintainability).
Actors are popular in Scala because of Akka (which presumably is in turn popular because of the support it gets from Lightbend). It is, not however, the case that actors are overwhelmingly popular in general in the functional programming world (although implementations exist for all the languages I'm thinking of). Below are my vastly simplified impressions (so take them with the requisite amount of salt) of two other FP language communities, both of which use actors (far?) less frequently than Scala does.
MVars also get used surprisingly often.
core.async, which is at its heart again channels.
As an aside STM, channels, and actors can all be layered upon one another; its sort of weird to compare them as if they were mutually exclusive approaches. In practice though it's rare to see them all used in tandem.
Actors do indeed involve state (and in the case of Akka skirt type safety) and as a result are very expressive and can pretty much do anything concurrency-wise. In this way they're similar to side-effectful functions, which are more expressive than pure functions. Indeed actors in a way are the pure essence of OO, with all its pros and cons.
scalaz.concurrent.Tasks. In return for less expressiveness you get more composability.