> The expense of distributed method calls comes from the [need to] run all method calls on the place where the object lives
Which is exactly the same in functional as OO languages. If service A has some data, and service B needs to make use of that data, then service B needs to make a call to service A.
The OO/functional axis is orthogonal to the monolithic/distributed axis.
What's expensive is shared mutable state. Isolated mutable state is fine - it can live in the place where it's used. Shared immutable state is also fine, as it can be distributed once and then reused as much as you like, and there's no need to worry about keeping all the copies in sync.
Functional programming is all about avoiding shared mutable state, so it does have an advantage here.
Which is exactly the same in functional as OO languages. If service A has some data, and service B needs to make use of that data, then service B needs to make a call to service A.
The OO/functional axis is orthogonal to the monolithic/distributed axis.