There's the legal problem there of essentially developing an anti-sat laser. Not to mention the engineering problems of lasing through that much atmosphere while still retaining the power to vaporize.
I think I've mentioned that we need mad (though benevolent) scientists/entrepreneurs to push space development. Obviously, they would need island fortresses and hordes of redshirts to protect them from the special forces of nation-states. XD
Seriously, though, there's no avoiding space development becoming a serious issue. Launch sites and satellites are already critical military and economic assets and an elevator, once we build it, will be a nexus of supreme economic power. It's no good kicking the can and pretending that economic development of space won't necessarily carry important military and political effects. I think keeping our orbit clean is a cause for humanity's good and well worth the effort of convincing chronically paranoid nations to buy into it (or at least to not invade Poland or start WWIII over it).
Twinkling is not a new optics challenge and other optics applications have had to address it. There are ways to mitigate air heating, though obviously you can't negate it. These aren't impossible problems for the idea.