We've seen this movie a million times already, haven't we? I think this is my standard reaction to 99% of music "scandals" these days, so at the risk of adding to the redundance ...
First, it's a bad idea in general to take life advice from Sinead O'Connor. Brilliant musician, well-meaning person, a wealth of experience worth listening to, hell yes. The voice of reason in a debate about the "evils" of the music industry? Pass.
Second, if Miley was really so deeply inspired by Sinead and her iconic song and video, you'd think she'd react more along the lines of "thanks but no thanks for your two cents" rather than treating Sinead like dirt and ridiculing her past behaviour.
Third, what kind of apocalypse is upon us when Amanda Palmer comes across as the most sane person in a Twitter war/war of letters? Even so, her portrayal of Cyrus as a shrewd personality who carefully manoeuvers herself through the music industry is exaggerated (to be fair, Palmer is hardly the first to make that characterization and claim that Miley is a lot smarter than the average pop star). To me, it looks like Cyrus thought it would be a good idea to shed a few real tears in her new video (thx Sinead!!) and that's roughly where the inspiration begins and ends, i.e. hardly the work of someone who carefully maps out her every move.
Fourth, although she has every right to be pissed off about Miley's response(s), Sinead is embarassing herself by stooping to Miley's level because there's almost no way for a 47-year old to come out looking good in a flame war with a 20-year old, especially given the subject matter of Sinead's original letter. Again, see #1.
Fifth, child stars will grow up and rebel and do crazy stuff to get attention and there's really no reason to get upset about it because it's happened over and over in the past sixty years of rock and roll history and will continue to happen from now until approximately forever. Next!