a spacer on top of the stem is a good idea, although it's not really for added stiffness as much as it's to stop the stem from forming a cone instead of a cylinder at the top. If the stem clamp is closed to a smaller diameter than the steerer where it projects above the top of the steerer, it tends to concentrate the compression of the steerer onto the top rather than spreading evenly along the depth of the stem. This is not a disaster with metal steerers, but it can wreck carbon ones. Also, the conical zone creates an inclined plane which generates a force pushing the stem off the top of the steerer. It won't move if you leave it alone in the shed, but the cyclic stress of normal riding will tend to make the stem walk up the steerer, reducing the headset bearing preload. You can help to prevent this, whether you have a spacer on top of the stem or not, by retightening the preload screw to 4-5Nm after clamping the steerer in the stem. This adds preload to the screw without adding any more bearing preload, and so increases the thread friction which will reduce the possibility of thread precession under cyclic load.
This is what I wrote the other day: