These are idomatic and natural, as you probably know. My sense of it is that sans the original direct object, the original indirect object becomes the direct object. That is, "showing" is something you can do to someone. I don't think it's all that different from "Please take me to the the movies." "Please take me. "Me" is not the indirect object in the first sentence, as it would be in "Please bring me a glass of water.".
I don't mean "show" in the sense of "I'm going to show my horse at the fair." Maybe I'm wrong.
I've never heard "give" used as you suggest in your third example, but the first two are quite natural. (Little kids say, "gimme," but it's sort of an idiom. There's usually a specific direct object in mind.)
Another one like "take me" would be, "Please advise/apprise me of your schedule." Please advise me. Same deal as your examples, but without the indirect object.