Earlier quoted context omitted.
Another reason is that a lot of gold trading is and was happening between central banks. (and moving the gold physically is a pain, easier to have them all in the same location, that's what the FRBNY account is for)
That argument is countered in the article. I will leave it as an exercise for the reader to read it.
a) Until 1971, gold was regularly moved between central banks. The United States exchanged U.S. Dollars against gold and Germany made use of this. Obviously, it was easiest to just leave the gold where it was bought - in the United States. This was also where a lot of other central banks had (and still have) their gold, so it also made exchanges easier.
b) After 1971, trading gold might have become less frequent, and at the moment the Bundesbank states it does not sell or buy any gold at all. But still: Look at Switzerland who has sold a lot of their gold after they joined the IMF. By selling gold out of the US Fed vault, they could offer delivery at the US Fed, avoiding a lot of logistical hassle. Maybe the Bundesbank just wants to keep this option open, even though they don't use it right now. It would be stupid to ship all the gold to Frankfurt, then decide to sell it in a couple of years from now, and then having to ship it back to the U.S. for the buyer.
c) Until 1989, it made sense to store gold outside of Europe to avoid it falling into the hands of the Soviet Union should they decide to invade (as suggested elsewhere in this discussion).
d) After 1989 and until recently, no one really cared about this topic. So it was easiest to just leave the gold where it was. Moving gold is a complicated business. The Bloomberg article linked above really makes it seem easier than it is. Yes, gold doesn't take up much space, but because it is so valuable you can't just put tons of gold into one plane / ship / truck - no one will sell you insurance for such a huge risk. You need to transport it in smaller batches, organizing secure transport and insurance for them, keeping the transports as secret as possible for security reasons. Also, you need to have sufficient storage available at the location where you want the gold to end up. And - again - you don't want to store all of the stuff in a single space because you won't get insurance for too much gold in one building.
I am not sure which explanation is the right one. I also find it a bit strange that they seemed to go through a lot of effort in melting these bars to make sure no one can inspect the originals. But this doesn't mean that there is no innocent explanation for all of this.