Because it's density is so low. In fact, by a few million miles from the solar surface, the density of the corona is in the same league as the vacuum inside a television picture tube. Even though the atoms have an effective temperature of 2 million degrees, there are only a few hundred of them per cubic centimeter, also, they do not produce very much electromagnetic radiation to start with because most of it comes out as specific emission lines in the x- ray part of the spectrum. Only in the inner corona are the conditions favorable for us to view the corona during an eclipse, even so, its brightness is overwhelmed by the energy coming from the disk of the Sun itself where temperatures are far lower, but densities are millions of times higher.
All answers are provided by Dr. Sten Odenwald (Raytheon STX) for the
NASA IMAGE/POETRY project.