Note: I'm working on a far future sci-fi setting for a novel series which aims to blend elements of both "soft" and "hard" science fiction concepts. I'm aiming for the series to be as grounded and consistent as possible whilst still allowing some elements of speculative physics. Most places in the galaxy are well within a post-scarcity economy, and any group or in some cases individual can afford a fleet of automated construction and mining drones if they so choose. Stellar and planetary scale megastructures are commonplace, up to Dyson scale and in some cases even larger.
The seedy capital of a region of lawless space is a tower almost 5000km tall built on an Venus-mass planet in the outer regions of a star system (not a space elevator). The tower, which we can provisionally call the Spire, was originally intended to be constructed to geosync orbit, but events in the distant past led to the abandonment of the tower and its subsequent takeover by criminal/corporate groups. The tower has a base 100 kilometres wide and makes use of active support and materials such as carbon nanotubes in its construction, and has a population in the hundreds of millions if not low billions. Much of the internal volume of the tower is given over to vacuum train tubes intended to bring cargo up and down the Spire. The planet's crust is robust and geologically dead.
Having recently come across an interesting Isaac Arthur video on super tall space towers (up to geosync, using active support and carbon nanotubes), my question is that would such a tower like the Spire be feasible with access to these technologies?
Note: In this context, active support or an active structure is referring to the use of a constant stream of matter (such as iron ball bearings) to impart momentum within a structure to provide support, as in the concept of a space fountain. The main advantage is that this allows for very large structures without relying on compressive strength, with the main disadvantage being that constant power is required to maintain the matter stream.
Note 2: The tower serves as a kind of "neutral zone" for these groups, which largely self-govern themselves such as historical pirate enclaves, havens etc. Any form of combat within the vicinity of the tower is strictly forbidden and harshly dealt with.