I used to teach an Astronomy Lab as a grad student many years ago. Even with the school's 16" telescope, most galaxies were fuzzy, and the students were somewhat disappointed (the planets impressed them however). You're absolutely right, there is such a wide array in the electromagnetic spectrum, and our eyes only give us a small sampling.

In the old days, professional astronomers were gathering cosmic x-ray, gamma-ray, and radio telescope information also, but these days the technology is so far beyond what we had then.

I suppose to justify the funding to the average person, the "image processing" is necessary (plus it also gives all of us a pretty good thumbnail sketch of what's going on out there...supernova, galaxy, quasar, black hole, etc.) The James Webb is quite an improvement on the Hubble, yet the Hubble was also quite revolutionary in its day.