But I can't think of a single use for wax slugs (or the guys other specialty, "cut shells") that a conventional slug would do even better.
The do have a purpose.
Back in my LE days I was on the bomb squad. Part of our duties was to support our newly formed SWAT team (we called them CRT).
We would make various breaching charges where as you could cut a door way in a way assuming you didn't want to use the door.
But if you wanted to use the door, and it was locked they had to have a means to bust the lock.
I loaded show gun shells with wax and fine sawdust, (similar to cream of wheat.
You poke the nose of the shot gun a few inches from the lock, touch it off, it would remove the door lock. The wax/saw dust mix would come apart cause little damage past the door.
Worked a heck of a lot better then normal shot if you didn't what to hurt anyone inside.
We also used the shells on our RMI (bomb robot) that came with a Remington 1100 mounted on the arm. It would disrupt suspected package that water (steam) wouldn't but didn't travel further out putting others in danger.
I also made electrically fired shotgun shells with the same mixture for our de-armors.
Having said all that, I'm now an old retired has been and haven't been fooling around with non conventional shotgun shells.