In an action/scary movie where the Hero says this to his partner/friend/sidekick- often but not always a woman- do they EVER wait there???
Doctor Who has been telling people that for nearly 50 years.
You’d think he’d learn.
Of course not. Why would they? 
I think Newt in Aliens waits when told.
But if they actually waited there, they wouldn’t be able to distract/knock out/kill the Bad Guy when the Hero is facing Certain Doom.
You have to understand that The Hero never really wants the Basically Useless Sidekick/Deadweight to “wait there”. He wants them to get bored, try to find him and save his life. This gives the Sidekick the self esteem/purpose he was missing until that moment and The Hero another chance to fight again.
If he survives his Encounter With Destiny, you can bet that The Hero will be a mite ticked off when he finds out that the Sidekick decided to indeed just “wait there”.
True, but when Ineffectual Sidekick does NOT Wait There and pursues Hero, I.S. almost invariably trips over something or falls in a hole and twists his/her (usually her) ankle, thus becoming more of a burden/nuisance. Or sometimes I.S. gets captured by alien/monster/bad guy because the evil one circled back around after leading Hero on a merry chase. Then you have the confrontation/square-off/mano a mano between Hero and Bad Guy while I.S. has a knife against his/her neck.
My favorite example of this is in the first *Mummy *movie, when O’Connell tells the warden to “Stay here, I’ll go get help.”, when the ship is on fire, and then jumps off the ship. For a second, the warden actually does stay put, then comes to his senses and jumps off as well.