Earlier quoted context omitted.
Who says attackers must use home or small office connections? Why can't the data be exfiltrated to a top tier data center with excellent peering?
But consumer/corporate demand for bandwidth is what should ultimately drive increase in data center bandwidth. Another point is defeating monitoring. I am sure the NSA (or Google/Facebook) could not notice 1GB of upload, but I like to think that uploading 1PB of data would make all sorts of red lights flash in they network security control room.
Most bandwidth is used sending many copies of the same content. Attackers aren't going to be interested in downloading the popular video 100 million times, they're just going to grab the logs which are nowhere near that size, and although large it's not implausible that even the best security teams wouldn't notice until it's too late.
There is no hard rule that the leaks need to come from the same central database either. That is unlikely considering the fact that large scale services are already, and necessarily, distributed. Imagine thousands of attacker hosts receiving from thousands of compromised hosts.