'Edit Edge Flow' equivalent in Blender? I'm a professional Maya user that switched to Blender less then a year ago. 
The "only" thing I really struggle with is the command "edit edge flow" that most 3d software have.

Here's an expample in modo: https://www.youtube.com/watch?v=I-4_U8ceIqM

Essentially, I think the tool works by looking at the average of the normals and adapting the edges or vertices to the area flow.

Something similar is the smooth vertex, but it doesnt smooth the vertex, it pushes the vertices in a way that follow the area flow: 

  

If we take this as an example, let's imagine we remove the 3rd dot. If we then add back a dot, its position would be changed and placed into a straight line, breaking the flow. With the command "edit edge flow" on that point, we would have the position back to normal. This would work both on an area or on a single point.
For your specific example Subdivide Smooth seems to be the answer.

For everything else there is Smooth Vertex that you already know or perhaps Laplacian Smooth, if you need finer control over mesh volume.