Grab a plank or any other long, relatively firm object. Hold it straight out to your side. Now hold it straight up. Now you see why it is more far fetched. (Edit: actually, just try it with your own arm for 30 seconds or so)

Not only is it far harder, but it doesn't take much length before even quite solid objects will start bending massively and exerting far more stress. E.g. doesn't take more than 150kg or so before the steel weight bars at my gym has a noticeable bend.

We still do not have materials technology advanced enough for a regular space elevator. Trying build one where gravity is actively working in a direction where there's no support seems unlikely to help matters.