P.S.: to provide a more visual reply, please have a look here, as you asked for a smooth result.
Clip
https://www.amazon.com/clouddrive/share/XQMCO4KB5TPur8OCh0Gg3ldqtSbvh0ABW5ey1yuEv0D
As a side note:
Phong shading works by taking one Polygon Normal as well as its neighbor, and transition between these. If you just apply more polygons, while the new points of these polygons follow the edge that was there already, the edge will have less influence and the results are typically less pleasing. In some cases it turns a fairly nice sphere into a disco ball with clear segment edges for example.
https://help.maxon.net/us/#TPHONG
The Normals in the help content are shown as arrows, one per polygon.
In the clip I have used a sub division which allows for a straight subdivision, as the Edge-Cut would do, but in comparison also a “Smooth” version, as the Subdivision Surface (ex HyperNURBS) would have created.
In comparison, the Edge-Cut fails to smooth. If done only a little bit and then smoothed, the results are anything (as shown in the last part of the clip above), but not straight or smooth (as in round).
I hope that helps to see the inner workings.
All the best