Thus does the amount of material not matter as much in a crane.
For wind turbine towers the material cost can be >>50% of the installed cost.
* The margins for cranes are thin and steel is expensive.
* Thicker steel is harder to work with, increasing manufacturing cost.
* Each kg of dead weight may decrease the performance of your product, e.g. max. Live load. This is especially true for the jib.
* More weight at the top of the crane may necessitate a sturdier structure below, amplifying cost even more.
* More weight may require more ballast blocks, which are costly (especially transport)
* More weight means higher transport costs
* More weight means more wind area, which is the critical factor for high constructions.Interestingly, wind/storm loads are oftentimes the limiting factor for the configuration height of a crane.
This is because, when adding another tower segment, not only the total area increases but also the wind forces. The other loads stay roughly the same
This is the reason why bottom-slewing cranes, which are commonly used for small buildings, sometimes are built with solid walls. Top-slewing cranes, which are used for high buildings, always use a steel framework.
At the limit the failure of your statement obvious. If instead of a thick walled wood tube hundreds of feet tall this structure were an orders of magnitude wider cylinder of thin plies the same height it wouldn't even be able to hold itself up, it would flop over, tear and all fall down under its own weight if not from manufacturing variances then from the wind and differential expansion/contraction from the sun and if by some miracle it survived that it would flop over
The material has to support itself and tolerate undefined small (relative to the main load) loads in other directions as well as point loads from fastening it to whatever you are using it to bear the loads of, going all in on "large and thin" fails to optimize for this for more or less the opposite reasons that going all in on "solid" does.
Frankly your comment disappoints me. wizardOfScience gave a _great_ answer, that would make any solid mechanics professor proud.