North by Northwest/Headscratchers

North By Northwest

 * The classic scene in North by Northwest where Cary Grant is chased around by a crop duster makes no real logical sense: having lured him to a secluded area to meet with a nonexistent person, why would the bad guys try to kill him in this fashion instead of having one of their people he hasn't seen yet walk up to him and then shoot him?
 * Alfred Hitchcock was fully aware of this during filming, but correctly predicted that the audience would be so invested in the film by that point that they wouldn't stop to think until after it had ended.
 * Hitchcock is, after all, the one who first spelled out the icebox moment.
 * I always assumed they wanted to make it look like an accident. If Cary Grant was found with a bullet in him. the police would start questioning the last people he spoke to, and their cover could be blown.
 * Obviously, Rule of Cool applies in full.
 * The above scene also makes no sense on another level: wouldn't the bad guys ask themselves why Roger Thornhill is traveling to the middle of nowhere to meet George Kaplan (at a rendezvous he thinks Kaplan arranged) if he really is George Kaplan himself?