My main concern with adjusting the mesh this way is the way other user-defined nodes would be adjusted from their set height in order to give the smoothed appearance.

Generally I work with a set of points from the surveyors that define the measured heights at specific points of the site. If I created a mesh of these points and I were to adjust one to the correct height using your proposed method, all the surrounding nodes would also be adjusted slightly away from their true measured values, which I wouldn't want. These need to stay static regardless, and only move if I manually adjust them.

I would prefer if you could create and adjust all the nodes individually, like you can the moment without affecting any others, but enhanced by having some kind of optional automatic interpolation (smoothing) in-between to prevent the jaggedness in section. The orange line below shows the smooth interpolated line.

It could also be quite a cool feature to be able to control this per individual node, as well as over all nodes, perhaps in the height adjustment pop-up dialog.

It's about time the mesh tool was updated generally as it's more-or-less identical to how it was at least back in AC6.5 and probably before!