I think it would be easier to work with specific cases, and then see if we can come to general suggestions. I think it happens to me for a bunch of reasons, one of which is literally the pressure of time, but the other is because of my training all through school to lead them to the answer rather than to find out what they're thinking.
Old habits are hard to break.
Of course, modeling a solution method is a valid way of showing a student how to think. Interestingly, I find it easier to try and find out what students are thinking when I mentor our Problems of the Week. I'm not sure why. Thanks for making me think about this.