Can’t speak for other eaters of “baby” carrots, but I used to buy them specifically because I was too lazy to wash and chop my own carrots. Washing slime off multiple baby carrots would be more work than I was trying to avoid in the first place.
(I do now wash and chop my own carrots, and I hate every minute of it. It is my least favorite morning activity.)
I immediately open the bag and leave it open in the refrigerator so any moisture can evaporate off. If you eat them within a week or so they don’t dry out too much, and it circumvents the slime problem entirely.
I’ve seen baby carrots stored in ice water, in a Tupperware container. You’d have to change the water often. I roll up single servings in a dry paper towel and store in a big zip lock bag …they keep about a week.