I created a svg in inkscape.
and imported it in blender.
Edit mode, with the display of handles turned off looks like
Selecting the curve by selecting one vertex and and pressing ctrl-L and pressing E to extrude it, restricting it by pressing Z does only result in translation.
I expected the mesh to become like a strip/band/wall.
The extrude curve menu that comes up shows some alternatives
...but changing to something else than translation here does not result in anything.