Ashtanga takes a very long time to teach you the depth of "correctness" that you can find in every pose, if it does at all: from your toes through the knees and hips to the back and spine and breath and shoulders your fingertips and your gaze (and we haven't even mentioned the mind), it is simply very hard to teach so much when you are moving through so many asanas! What I mean is an "ideal" Ashtanga practice certainly teaches you the above; however, in reality, this requires you to be lucky enough to have a great, consistent teacher, and many years to learn the details of every pose. For a home practice, very few of us are knowledgeable/insightful/observant enough to teach ourselves what the tradition knows.) An Iyengar class is like a localized, focused boost to your practice, diving deep into one "topic" and enriching the rest of your practice for it.
Many years of practicing Ashtanga alone may get you there, but they may very well also develop a practice that misses small adjustments and big insights (and in the worst case, injures you). While I strongly disagree with your comments about Ashtanga being "brutal", or that it sometimes avoid the ease, with a lot of rounding of the back etc. (a good yoga practice is never forceful to your body's tissues in a damaging way, which is what "brutal" sounds like; it is a force of will, and concentration, that is required. Which is why it is an inherently spiritual practice. Staying where it is hard to stay, focusing on breath and alignment and stilling your mind: both when the body moves, whispers, whines, trying to get in the way, and when it moves out of the way and it is your mind that tries to run away, through the fields of its projection), without careful teaching Ashtanga can lead you to be "greedy" and try to push forward, deeper into known asanas or into the next series' asanas before you are ready.