What if public schools asked those kinds of questions at the beginning of the year? Yes, it might be more time consuming, but wouldn't it serve everyone better?
When I was student teaching a couple years ago, my mentor teacher sent cards home on the first day of school soliciting information about the students from their parents. She is an uncommonly excellent teacher, though.
I think a good & experienced teacher WILL know these things about their students. DD's part-day kindergarten teacher, who had 42 students, knew DD well enough by the 2nd month of school to tell me at our first parent conference that she suspected DD was highly gifted.
