Because 1. Leggings would make burns way more of an issue as they are practically sponges. 2. Leggings are not meant as professional work attire unless you wear a dress over them. You already get enough creepy customers as it is...

It may have something to do with preventing/mitigating burns. It’ll absorb the hot liquid and stay pressed to your skin. This would happen anyway with even somewhat loose fitting jeans, but that’s the only reason I could think of off the top of my head.

You're allowed to wear them under a dress or skirt so I think it's just that it's seen an inappropriate

I’d guess because they’re seen as unprofessional and the burns thing

Leggings are not professional attire and the dress code wants partners to dress nicely.