Space is not empty. Satellites have to be boosted all the time because of drag. Massive panels would only worsen that. Once you boosters are empty the satellite is toast.
On Low Earth Orbits (LEOs), sure, but the traces of atmosphere that cause the drag disappear quite fast with increasing altitude. At 1000 km, you will stay up for decades.
for a reasonable temperature (check my comment for updated calculations) the height of a square based pyramidal satellite would be about 3 times the side length of its base, quite reasonable indeed. Thats with the square base of the pyramid as solar panel facing the sun, and the top of the pyramid facing away, so all sides are in the shade of the base. I even halved my theoretical cooling power to keep calculations simple: to avoid a long confusing calculation of the heat emitted by earth, I handicapped my design so 2 of the pyramidal side surfaces are reflective (facing earth) and the remaining 2 side triangles of the pyramid are the only used thermal radiative cooling surfaces. Less pessimistic approaches are possible, but would make the calculation less didactic for the HN crowd.
Here's a big one: you can't put radiators in shadow because the coolant would freeze. ISS has system dedicated to making sure the radiators get just enough sunlight at any given time.
this system would not be given such an orbit. Its trivial to decrease the cooling capacity of the radiators: just have an emissivity ~0 shade (say an aluminum foil) curtain obscure part of the radiator so that it locally sees itself instead of cold empty space. This would only happen during 2 short periods in the year.
The design issues of the ISS are totally different from this system.