When you create a new work based off a public domain work, you own what you added to that work. If your adaptation happens to be extremely successful, that effectively recopyrights the character, because the version people care about is the one you own. If someone else wants to use the public domain character, they have to aggressively distance their use of that character from yours.

Disney spent decades re-imagining Europe's folk tales[0] through his lens. Their movies are the ones people think about when you mention Snow White, Cinderella, Pinocchio, etc. Notably, the visual designs are unique enough to get independent copyright protection. So independent uses of those characters don't look like themselves.

This, BTW, is why anyone who wants to renounce copyright over their creative work should opt for CC-BY-SA and not a public domain dedication. Share-alike clauses prevent this sort of gradual appropriation.

[0] as filtered/censored thru the Brothers Grimm