As I understand it (see: not at all), if you leave a spaceship with no suit on, you’d get baked like Marie Curie’s ovaries from the radiation. It’s mainly our atmosphere that protects us from most of the nastiest stuff. Would a giant cable reaching from Earth all the way to a platform outside the atmosphere become dangerously-radioactive over time? And if so, would that eventually cause the entire planet to get radioactive over hundreds of years? Kinda like if the hole in the Ozone layer were replaced with a Mario pipe.

And if that is the case, maybe we could forget the elevator aspect of it and just aim for a free eternal source of radioactive energy, like a really shitty Dyson sphere 👀