Cyanoacrylates (super glue) is very brittle which doesn't work on
flexible plastics, which includes some wall warts. I've glued them in
spots around the perimeter, only to have the case pop open when I
dropped the wall wart on the floor. I suspect more glue would be
better, but have never tried it.

There are "toughened" cyanoacrylates which are supposed to be better
about this... the ones I've seen apparently include some extremely
fine rubber particles or other fillers. Most of the big glue
manufacturers seem to sell one variant or another of this.