My experience traveling with a cane was quite opposite. Going trough security I got pulled aside, hand scanned, patted down and totally humiliated. They did let me board the plane first though. In general, people are nice and open doors.
You don’t have to have a cane for that to happen. Anyone can get pulled aside. It’s happened to me numerous times. If you really want the experience travel to a place on one airline with a one way ticket and back with another airline without luggage. I did that going to Chicago for a day trip and got check at security and was again pulled aside when boarding the airplane. Four very thorough security checks in one day. They had my name on a list.