I'm a high school English teacher who asks students to read poetry, including the works of realists like Robert Herrick, so I'm a bit biased here. With that out of the way, I think there are a bunch of issues to dig into in this question, and I hope to just tackle a few:

1. Charisma and Agendas. Without question, Mr. Keating is a problematic teacher-figure in film. He takes a job working with children, trying to breathe life into them before they shuffle out the door, conforming to the values of their parents and the institutions that have carried them--generationally--into success. His self-appointed mission is to interrupt that process by communicating to them, Day One, that they are following their parents down a Wrong Path, and that literature is a means of switching onto the Right Path. The ethics of this are dubious.
2. Literature As Problematic. There's no shortage of people in the world right now who want nothing more than to keep literature out of the hands of children. The quality of literature is that we do not merely consume it, but that we interact with it. Poems and books can shape our thinking, and when we're vulnerable, we're vulnerable to literature, too. Realists dealt with the isolating nature of the industrial world, and it's too common to assign blame to artistic expressions of problematic circumstances rather than the problems themselves. Neil absolutely sees himself in the art because it's true. So it follows that asking teachers to shield minds from literature is equivalent to shielding them from truths like "We're all mortal," and "Do things, now."
3. Expecting the Unexpected. If I've learned anything in almost two decades of education, it's that talking to teenagers in figurative terms or moving into the philosophical discussion of the abstract means that those who are actually listening and processing what you say are very likely to apply what you say unexpectedly. Placing responsibility on Keating--or more specifically, blame--requires us to say that either (a) he should have expected this could happen, or (b) regardless of if he expected it, he owns a piece of it. I have to work with pretty subtle degrees or shades of the term "responsibility" to accept the notion that an English teacher bears responsibility for rash decisions of children who are suffering from isolation borne from familial pressures.
4. Characters as Vessels. If we consider Neil, Keating, the administrators, the parents, all the characters as fictional figures rather than real ones, it helps us see them as vessels representative of the values of the time, rather than simply as make-believe people with motivations. If we assign Keating blame, as a vessel of anti-authoritarianism, in the decision of the Self Destructive Victim of Authority character, then that's highly problematic--it establishes a theme of the story that empowerment is dangerous and the right road might just be to acquiesce to Authority and to bide time. The urgency of Keating here, not as a literal one but as a symbolic one, speaks more broadly to the need for people to develop their identity early in life as part of the formation of their character before they are swallowed by the Leviathan. The truth is, the Father figure is also in crisis: he acquiesced to his own father, and his father before him, and the institution of the school reflects the broader society that isolates people to the point they don't recognize the value of their own children or the value of education itself as anything more than a path to financial excess and placement within the machine. Fundamentally, something the American realists saw in their poetry.