By that time, many of the planet's major cities and governments had been destroyed.
Yet every city we see in the future has recognisable landmarks from our time.
Paris, SF, new orleans, cambridge.
Noone ever says lets go to the crater where london used to be.
The trek writers are now saying that every episode that featured time travel created a parellel universe that was very close to the orignal, but with subtle differences.
So basically every fuck up and contridiction in established history can be blamed on Kirk's wacky adventures through time and space, and also those who followed him.