OK, I've wanted this for years and it's still not available.
I don't want paper statements. From anybody. I don't want to file them away. I don't want to scan them myself. And I certainly don't want to pay someone to do it.
I want electronic statements that are secure. I want them backed up regularly. I want them authoritative - one of the big reasons that I don't go electronic is that I figure the original statements will carry more weight with the bank, company, etc. Or the court, if it comes to that.
I don't want them alterable. If the bank has an error on their statement, I don't want them to be able to be change it. If I have 2 statements for February 2006 - the right one and the wrong one - that's OK.
I want this to be online for as long as I'm alive. Having my own local copy is fine but the hard drive in my laptop crashed last August. I was and am better about backups than most people but I still lost some data. So I want somone else doing the backup, too. And I don't want to pay anything for it.
I have an account at Charles Schwab. They started charging for paper copies of transactions so I went electronic. Which is a pain in the neck. There are class action lawsuits filed about stocks that I owned years ago. They (courts, attorneys, company, somebody) know I was an owner because they're mailing me. But now I have to show them when I bought the stock, how much I paid for it, etc. This is seriously not fun.
Schwab pokes at me from time to time to go to electronic statements. I have no idea why I would ever do this. They only keep statements online for 18 months. Which means that I'm supposed to downloading, backing it up, etc.
Things are getting better with gmail. Now the electronic stuff can come in and just sit in a folder somewhere. Google takes security seriously enough to require encrypted access. But there's no guarantees about reliability or availability.
My house in Portland was built in 1914. It has a mail slot beside the door. You're going to have to break into the house to steal my mail. A lot of other people have their mailbox on the parking strip. If you want to steal their mail, well, you're going to have to open the mailbox. It seems like there are a lot more people in that situation than mine. A few years ago, many people thought it was crazy to have electronic statements. But now, with identity theft, a lot more people would be willing to do it.
So what you should do is start up a company.
More on that later.