I had the same treatment you are describing when getting my H1B visa in the USA from the UK. And things got even worst when my employer started to apply for greencard, and so I just left the USA.
From a private sector perspective, I had more things paperless available to me in 2003 - when I moved to the USA - in the UK than I did in the USA. And during my time in the USA, I was able to run all of my UK business and government transactions online.
Australia is the same. If you want any sort of Security Clearance (i.e. you want to work for the government), you need papers proving where you have lived for 10 years. If you've lived in a couple of share houses and thrown out all your old bills, this can be almost impossible. (Yes, you can sign a Stat Dec, but it's frowned upon).
Presumably this is for tax purposes, in case they're audited? If that's the case, your friends are out of date - HMRC (the tax authority) has accepted scanned documents in place of originals for some time now.
It's taken a while but things are getting there.
I actually do have a few "paperless" services here (DSL, for one), and it's actually biting me now because there are still organizations that absolutely require paper documents to function.
Banks are just as guilty of this as the government. Try opening a bank account anywhere without a paper copy of a utility bill to prove your address.
The more paperless we get, the tougher life gets when trying to deal with the few holdouts who need to see your papers.
As a current UK resident I find that surprising as a high proportion of the people I know have shredders at home, they're very common.
I'm going through the process of settling here in England, and as part of my visa application they asked for 2 years worth of paper bills (originals only, no copies, downloaded statements or printed scans). "What???" screamed my inner-American. "Who would keep that around?" I had exactly one phone bill sitting around and it was a month old.
Explaining this ridiculous requirement to everybody I could find over here, I was met with nothing but: "Of course. Why would you throw something like that away? I think you're legally obligated to keep all paperwork for at least 3 years. I still have bank statements from the '80s up in the loft." Nobody believed me when I explained that lots of people in the US had paper shredders in their homes.
No sympathy from Her Majesty's Immigration Services either. I stand a pretty good chance of having my visa application rejected as a result of my American inclination toward paperlessness.