Besides the obvious things such as lack of buildings you can enter and the crash physics, I think one huge thing that is missing from a game like this is the ability to tie someone up and throw them in your vehicle.
Kidnapping, basically. You could basically do it in Red Dead Redemption - you'd tie someone up and put them on the back of your horse.
It'd create so many fun scenarios. There could be extra missions where you hold them for ransom, or hitman missions where you stick them in your boot and drive up into the hills and shoot them up there. It'd be great online! Imagine killing bounties this way.
I'd love it in the game, but sadly it's not. It's one of the many things this game lacks.