I've been looking deeper into the tower structures in Prime Base. These are the same shape as cooling towers:
https://en.wikipedia.org/wiki/Cooling_tower https://en.wikipedia.org/wiki/Hyperboloid_structure
https://en.wikipedia.org/wiki/Willow_Island_disaster
https://www.youtube.com/watch?v=eoyimyyekB8
This all seems to indicate that this type of structure is particularly poorly suited for the needs of Prime Base.
First they are difficult to construct and require specialist engineering and labor as well as equipment. This means they would be expensive to build and need a lot of specialist to
From what I can determine these structures would respond poorly to asymmetrical stresses on the floors, as the floors would be connected to the cylinder walls which would bear the load. I can't find a structure of this type that is loaded with intermediate floors. It seems this type if structure is capable of bearing a load on the top that pushed downwards but not the type of load that would be generated by load bearing floors, such as proposed in the canon design.
The use of giant towers also requires a giant space. This is even more true since all three are in the same cavern. I don't recall the exact size of the cavern but it must be around the size of a football stadium to hold all three cylinders. Such a huge space presents all sorts of issues in construction, debris removal, security, safety after construction and probably other things as well. By getting away from the vertical towers this makes a lot of other options available.