You can do all that with CSS too 
It may be ~4 lines but definitely do able. Plus since you can enable multiple styles now, you can simply have one for category alterations and keep it enabled 
My point was, no one is really customizing this icon today. So we’re bikeshedding here. “It would be great if we use X or Y or Z” without actually seeing people using it.
I simply showed how easy it is to customize the icon. The background image is a bit harder, but by a smudge (I haven’t tested this, but it should be relatively close).
.badge-category i.fa.fa-lock:before { content: ""; } /* remove the existing icon */
.badge-category i.fa { background-image: url('...'); background-repeat: norepeat; padding: 6px 6px 6px 6px; } /* assuming 12x12 icon */