Yes, gluing the 2 pieces of the plastic bar would of course improve the strength. Originally, I was going to do that. I also considered reinforcing the bottom of the plastic bar by gluing a small strip of poly-type plastic to it. I also considered gluing the bar to the cover using a flexible cement. Finally I decided that the sticky foam tape would be enough. I have had very good long term [several years] results with this product attaching all kinds of things to all kinds of surfaces. Getting it unstuck after months is the issue.
I DO wear braces/suspenders AND a belt [for some outdoor sports]