Sometimes my dog gets a nasty-smelling discharge of mucus from her vagina, so at least the licking 'disposes' of it so that it doesn't dangle between her legs like a strand of snot. She's been spayed and the vet doesn't think she has an infection, though I've never managed to get a urine sample from her to confirm it, so the mucus might be caused by what's left of her reproductive hormone cycles.
She likes me to lift her up and cuddle her, and her favourite position is to have her rear legs splayed around my waist, her chin on my shoulder and her bits pressed against my abdomen, so I often have to change my top afterwards because of the fishy stink and the shiny mucus stains.