Because Moffat says so...

According to the RadioTimes Moffat was made  to answer some questions arising from the very, very obvious plot holes of "The Angels Take Manhattan". But it's hardly worth reading the article, because things do not really get explained. I mean, all he has to say about why the Statue of Liberty was able to move through New York without being noticed is 

"In those terrible days, in that conquered city, you saw and understoodonly what the Angels allowed, so Liberty could move and  hunt as it wished, in the blink of an eye, unseen by the lowly creatures upon which it preyed. Also, it tiptoed."

That's not an explanation, it's a statement. We know that being watched the Angels cannot move and no matter how fast they are, or  how much they do not want to be perceived, moving from Liberty Island to central New York cannot be done without being seen, by someone, at least once. And then they had to stop and become 'obvious' to the citizens of the city which never sleeps.  Therefore, it's not possible. 

And the back-up-story of why the Ponds cannot travel to the UK, or any other part of the world to be picked up by the Doctor there instead is not better...

Maybe the best bit is RadioTimes' comment on how Moffat is not really dealing with the paradoxes created by the Pond's farewell episode:

"If your head hurts now, wait until someone asks Moffat what happened to the whole 'an image of an Angel becoming an Angel' thing. That's a lot of dangerous New York postcards, right there..."

So, dear Moffat, simply admit you've done a few mistakes there. We'll  forgive and forget. And Sir, please, promise to put more thought into an episode's plot in the future.