With all this message passing, have anyone experienced the network becoming the bottleneck !?

In large Erlang applications, the "send to multiple peers" broadcast tendencies of its message passing can indeed cause the network to become a bottleneck; so can the default chattiness that a lot of Erlang application developers assume for their app behavior.

Fortunately, there are lots of simple-to-apply patterns and solutions when you get to that point, for example the excellent Partisan library: https://github.com/lasp-lang/partisan