In the US, as well. In fact, it's been advancing for a few years now. It also eliminates the huge cost of order new letterhead whenever the company changes telephone numbers, changes/adds/closes locations, etc. It's curious that this otherwise desirable "green" practice wasn't taken into account when the PBS was being designed.
Again, don't get confused between bank statements and other types of information.
Also, do you have a better suggestion of how to submit information in a way that is verifiable from a financial institution? In some countries, there is a large black market in documents and identity fraud is ripe. That is part of why UKBA the document verification departments. What is to prevent someone from totally making up some account information and printing it out on their printer? Especially when it comes to on-line statements, it would take me 5 seconds to manipulate a web page and print it out that showed my account balance being super high.
The rules continue to flucuate. For example, the amount of evidence required for a FLR(M) has been reduced dramatically the past year, due into part to people getting less official post.
If you have another way to help ensure that people have the money they say they have, that works globally, I think we are all ears.