Is there anything fundamentally holding us back from building one right now? I mean there's the obvious problem that nobody has a good reason to build one, and only a hand full of entities have the funding to do so. But the engineering challenges seem to be on the level of building LHC or ITER: not nessesarily easy, but very doable.
For a small-ish cylinder that might be enough. For a cylinder that's multiple kilometers long we would want to do asteroid mining and rockets engineered to bring stuff up cheaply (at the expense of loosing a few rockets, loosing dirt is a lot more acceptable than loosing billion dollar satellites).
There is still signifficant air drag in LEO that would get it down rather quickly, ruining someones day on the surface.