Is a huge heat shield with some aerogel or something behind it to contain the heat that couldn’t be turned into energy

The first line of the Project Rho page:

NO, for the millionth time you CANNOT get rid of the heat by turning it into electricity!

And yes, we're assuming the radiator is way far away on some kind of tether. Again, first few lines of the page. But the aerogel wouldn't make a difference, it would actually hinder this system.

I will bet money that at some point someone argued that communications going through satellites in space would be unpractical because of engineering and technological challenges, the stupendous cost of getting stuff up there, and monumental maintenance costs compared to just having some lines going through some street poles.

No.

No one was saying this.

People complained about the engineering concerns, but engineers recognized it was physically practical... in theory.

But we are talking about physics now. Doesn't matter if you're a transcendental AI or not, you cannot engineer your way around thermodynamics, and we are talking about just one problematic system.

The only tech that would make such a dramatic difference (that's on the horizon) is a space elevator, as it circumvents the rocket equation entirely by 'pushing' against the Earth. But this is really, really, really hard.