It's like saying "Warp drive is possible" then saying all you need to do is build a ship that can manipulate the fabric of spacetime. Well of course that's all you need to do.
Sure, producing carbon nanotubes is easy. I've seen them make the it in a lab. It's making the tubes to spec and making thousands of miles of the stuff that is the hurdle. It's the equivalent of asking computer engineers in the 60s to mass produce 22nm CPUs with billions of transistors. Can it be done? Sure. In about 50 years.
Why would they be similar? The space station is only in LEO. That's not remotely comparable to geostationary orbit, or the Van Allen belts.
Fortunately, shielding is a lot cheaper than on anything a rocket carries.
The first few years will enable 20ton payloads without humans [radiation
tolerance an issue for the two week trip]...
Radiation is not a problem for tether climbers, as the designers will
incorporate this threat into the design requirements and ensure operational
success through any radiation environment. Historic precedence supports this
conclusion as the space community runs spacecraft in all regions where the
space elevator will be operating. However, when people are included in the
tether climb [after some years of robotic success], the radiation problem
becomes an order of magnitude more difficult. There are many ways to reduce
the radiation and shorten the trip, which will have to be incorporated when
the human element is added.
There is a fairly long section on debris. The authors note that significant debris only exists in low earth orbit. They think the chance of collision is small, but large enough that the situation needs to be monitored. They think debris can be tracked and that if a collision were forecast, the cable could be moved. Also, they think space faring nations should be tasked with removing some of their junk from orbit.
But shielding seems to be doable with pretty thin layers of metal.