Because the turn based combat is an abstraction of real-time events. Characters in D&D don't stand around waiting their turn to take action.
Yes. RTwP is an abstaction of real-time combat as well.
No one is standing around in TB, just as no one is standing around when you press pause in RTwP. Turn represent individual character's actions - afterall it is combat of individuals, rather then a Team Commander Simulator. Turn order represents their reaction speed (character A has quicker reflexes so he will get to act before character B does). Reactions allow characters to act throughout the round.