It becomes a question of how good is good enough for your application because even a theoretically perfect design will have some variation in the real world..
3d exposed copper is normally done by soldering a piece of metal to the board and calling it an antenna.
A standard monopole antenna over a ground plane has good rotational symmetry but isn’t good for UWB bandwidths. A conical antenna over a ground plane or a bi-conical antenna in free space would be UWB equivalents, they give a symmetrical pattern over a full 360 degrees (in a plane, you still get variation vertically). However they add a lot of mechanical complexity to the design.