I would like to draw a 2D shape and extrude it axisymmetrically (rotational symmetry). Is it possible?
I think the Screw Modifier is exactly what you want.
This kind of tool is available in many 3d programs. It "screws" or "lathes" a profile around any axis that you pick. Here i've screwed but not used an AxisObject - in this case it uses the Object's own world matrix.
Here's i've picked an axis object, an empty, and rotated it. This is useful when Z,X,Y are not the desired rotation axis.