Perhaps this thread is about burned out, or self imploded, but I'll throw in my 2 cents. I would hope that we can all accept that there are certain basic techniques and principles that have proven themselves over time, and, that also are modified over time as new data come in. And, that there are some people that are more knowledgeable and expert than we are, certainly than I am, and that these are people who should be listened to. It's not all just however I may "feel" about something, based on who knows what.
So, my sense of the "accepted" view is that an ice axe is necessary safety gear on steep slopes, particularly steep hard slopes, such as ravine head walls, slides, and other similar pitches. Poles just won't work to stop yourself in you fall in such a situation. Of course you have to know how to self-arrest and practice it in benign conditions, but given this, your chances of stopping a potentially dangerous fall are much greater with an ice axe. If you don't hike in such conditions, then I don't think it's needed, but, in my opinion, tackling certain trails without one is taking on an unacceptable level of risk.