I think that the above reason is overstated. Maybe it's just because I don't make it a habit of falling on my back?

However, I can give you another reason or two why it's not a good idea, based on personal experiences.
- Very hard to draw safely if you need it.
- Potential for embarrassment. BTDT and have the T-shirts.
- Many years ago my Wife and I went to a restaurant in Harvard Square . I was wearing a sport jacket and waited until I sat down before removing it. When I got up, I noticed some agitation by the bar with the bartender and a waitperson. Only then did I realize that the wall behind me was a mirror and they had a view of the gun as I stood up before putting my sport jacket back on. Whoops #1.
- Back in the 1990s I was attending town meeting in our high school auditorium when I got up to speak and my jacket over-rode the butt of my gun. I heard gasps from the audience but just chuckled to myself. If someone reported it to a uniformed officer they would just be told that I was one of them.