You've never had a company tried to shaft you before?
Now that I can't access my statements with Avro, what if the next appointed energy provider claims a vastly inflated debt on my account, for example?
What if I need to provide statements to some financial organisation to indicate proof of my address, they often ask for utility bills, and the bills can be at most 6 months old.
As a side note I find it odd that your first conclusion is that people who think bills are important must be data hoarders.
About the only bit of completely unnecessary financial information I keep are the financial breakdowns of my wife and my monthly expenses on a historical basis, but considering a spreadsheet probably weighs about 9KB and sits on a 4TB drive and I do a new financial breakdown only when something financial changes (e.g. a different charge from a given company), which is maybe about 3-4 times a year.