Well you can... but only in the projected 2D plane.
I get what you are saying, that would require a 3D curve or 3D polyline tool.
As for vertical contours - there are several way to do this:
You can setup a series of workplanes (UCS) that vertically intersect the horizontal countours. Select each UCS in turn and then use the bezier or polyline tool along with the Nearest snap to snap to each line.
You can use the point tool. In Pro the point tool has a 3D mode and you can snap to 3D objects. You can then use the points to generate a terrain. Or you can use the terrain tool directly. Just remember to turn off all snap EXCEPT nearest on graphic.
Once you have a terrain you can use the Architectual section tool with specific section lines. Or you can use the drafting palette. With either you can create sections. Which can then be exploded and cleaned up if necessary.