You've shown a proposal, not a reality. (and the proposal didn't even mention a "shield" that I saw, but I may have skimmed past it). I didn't see a price tag, nor a timeline. Money can boost research speed, but not remove the need entirely.
Second, If the cross section of the earth is 1.2x10^14 m^2, one of these would...well, we don't know, because the link mentioned volumes and length (the 10k km is a potential "span length" and wasn't tied to being "one" of anything). I failed to find the cargo volume for a Falcon 9 or other rocket (everything is in mass) but I think it's safe to say that you're talking a lot of launches which clearly aren't trivial to do.
Third, and most importantly, you've just decreased the amount of energy coming to earth. You've not solved the problem, you've changed it.
I love tech, but I think it's worth noticing the ratio of times someone says "It's [just] an engineering problem" versus the number of issues that have been actually been solved in this way (seeing the problem, spending a boatload of money, seeing problem solved). Most of our industries are based on the fact that we KNOW they can grow into more, but figuring out how and the complications thereof are literally the work of countless lifetimes.