Slugs are hard to come by and expensive, more than a dollar a round. Bird shot is widely available and cheap. Look into the waxer a little deeper you may find that there is a reason your assertion may not be right. There is a physical reason the waxer distributes force differently than a slug. Some people use hot glue or just wood glue, but wax is much cheaper.
Seems to me a wax/birdshot slug might fragment on impact or shortly thereafter. Which means it might actually do more damage, or at least more widespread damage than a lead slug.
Though doing more damage than a lead slug to a person would be sort of the definition of overkill.
But I’m definitely not any sort of expert in this area.
I saw a lot of Youtube videos on making wax shells. I had never heard of that before.