Burring something for a few years is easy, but what about hundreds, thousands, ten thousands? The earth moves and this stuff is way more concentrated than anything found naturally. What if it hits ground water?
They have been trying to find something for decades and come up empty.
The whole infinite power from space argument seems problematic. Even assuming you just meant "a large, globally significant amount of power", I'm guessing that the inverse-square law and heat buildup would sink the idea. I can only imagine the dead zone surrounding the location where we beam petawatts of radiation down from orbit. It would make our worst ecological disasters look like a joke in comparison.
Heat buildup in general isn't the problem, it's heat buildup in the atmosphere that's the problem, and infinite clean energy would allow us to reduce carbon emissions to 0, as well as do lots of crazy geo-engineering that today isn't feasible because the cost of electricity is too high.
Jesus. Someone failed thermodynamics.
The problem isn't heat in the general sense of the word, it's heat trapped in the atmosphere. Heat trapped in the core of the earth isn't a problem at all, for example. Most human generated heat can be absorbed by matter on the surface and has a negligible impact on atmospheric heat. And if you had enough energy and low cost launch to space you could do things like cheaply send solar reflectors into space.
Nuclear waste is comparatively easy to handle. A single country is capable of handling its own nuclear waste and keeping it safe (as France does, for example). The same is not true of CO2 emissions and global climate, which require transnational concerted effort to manage.