George Lucas came up with that glad-you're-alive-but-I-won't-save-you-yet "Raiders of the Lost Ark" bit.
In the George Lucas / Steven Spielberg / Lawrence Kasdan "Raiders" story conference transcript, that moment's brainstorming development goes like this:

"(...)
GL — I'm worried that if he finds the girl...

SS — She's right back in the action again.

LK — That's good, because he has nothing else to do with her but take her with.

GL — I thought he would leave her all tied up. "Look. I can't take you with me, it would arouse suspicion. So I have to leave you here for a little while. I'll get you out later." If they find out the girl is missing, they're going to start searching everywhere.

SS — She says, "Let me out of here. Let me out of here." He tells her to keep her voice down. She won't, so he has to gag her again. "Look, I'm glad you're okay. It's a big relief to me. I've got a lot of things to tell you. But you're going to ruin this whole thing unless you just sit here and be quiet. You've been here for forty-eight hours, another three or four hours won't make any difference at all." He leaves her tied and gagged. That would be heroic. I like that.

GL — My only concern was that if he takes her, the Germans would be combing the countryside.
(...)"