This might be a question of personal preference. At the design stage I already find it more approachable to think in separated responsibilities, and it naturally translates to actors. Thinking about the app, it's much reasier for me to thin "send the message to the actor" than call that function that uses the necessary mutex. With mutexes, I think the separation of concerns is not as strong, and you might end up with a function taking multiples mutexes that might interfere. With the actor model, I feel there is less risk (though I'm sure this would be questioned by seasoned mutex users).

In this simple case they're more or less equivalent if the only task is limiting concurrency, but in general usage of mutexes multiplies and soon enough someone else has created a deadlock situation.

Extending it however reveals some benefits, locking is often for stopping whilst waiting for something enqueued can be parallell with waiting for something else that is enqueued.

I think it very much comes down to history and philosophy, actors are philosophically cleaner (and have gained popularity with success stories) but back in the 90s when computers were physically mostly single-threaded and memory scarce, the mutex looked like a "cheap good choice" for "all" multithreading issues since it could be a simple lock word whilst actors would need mailbox buffering (allocations... brr),etc that felt "bloated" (in the end, it turned out that separate heavyweight OS supported threads was often the bottleneck once thread and core counts got larger).

Mutexes are quite often still the base primitive at the bottom of lower level implementations if compare-and-swap isn't enough, whilst actors generally are a higher level abstraction (better suited to "general" programming).

You are using mutexes, they are on the Actor message queues, amongst other places. "Just use mutexes" suggests a lack of experience of using them, they are very difficult to get both correct and scalable. By keeping them inside the Actor system, a lot of complexity is removed from the layers above. Actors are not always the right choice, but when they are they are a very useful and simplifying abstraction.

Horses for courses, as they say.

Because actors were invented to overcome deadlocks caused by mutexes. See page 137. With mutexes you can forget concurrency safety.