One reason to unclip only the left foot, and make that a habit, is it will discourage always wanting to stop at the curb and put your right foot on the curb.

If you ride at all in traffic, being right on the curb encourages cars to make right hand turns in front of you, thereby cutting you off, and to sometimes come to close to you. They also tend to notice someone lounging against the curb.

I started clipping in when I was past 50 and it took over a year of accident-free riding before I had two tip-overs close together: one caused by a dog and the other when I was at an intersection with a 4-way stop. The "good samaritan" kept encouraging me to go even though it wasn't my turn, it threw off my timing and I tipped over. The good samaritan finally drove off after I was sprawled on the ground! As you mentioned, hurt pride was the only damage!