It won’t join if you don’t redraw both faces as pentagons, with your new point shared by both.
And yes, this is a tedious process that coupd be made into a single click process with a command that can insert a subD vertex.
If I was creating it, I’d call it _insertvertex, have it work in Mesh and SubD, be able to snap to midpoints of mesh and subD edges, near-snap to edges, and also be able to snap to rhino points, so you could do:
_divide (make five equal segments for example)
_insertVertex …click on the three non-endpoints
And get 3 equally spaced new vertexes, turning each adjacent face into an ngon.
Is there already a mesh command that does this? I don’t use mesh a lot.
Update: now that I think about it a little more, how about two commands: _insertVertex (automatically near-snaps on an edge, and detents at edge midpoint) and _divideEdge (prompts for number of divisions)