Making the pyramid arbitrarily long and sharp will arbitrarily diminish the heat conductance through the pyramid, so the farther from the pyramid base, the colder it will be and the less it will radiate.

So no, you cannot increase too much the height of the pyramid, there will be some optimum value at which the pyramid will certainly not be sharp. The optimum height will depend on how much of the pyramid is solid and which is the heat conductance of the material. Circulating liquid through the pyramid will also have limited benefits, as the power required for that will generate additional heat that must be dissipated.

A practical radiation panel will be covered with cones or some other such shapes in order to increase its radiating surface, but the ratio in which the surface can be increased in comparison with a flat panel is limited.

we are not discussing a schoolbook exercise, we are not calculating passive heat conduction of a pyramid heated to a base, since it's not a schoolbook exercise we can decide on the condition, we could put in heat pipes etc.

its CPU/GPU clusters, so we don't have 0 control on where to locate what heat generators, but even if we had 0 control over it, the shape and height of the pyramid does not preclude heat pipes (not solid bars of metal, but having a hot side where latent heat of a gas condensing to a liquid on the cold side and then evaporating on the hot side).

heat pipes have enormous thermal conductivities