I don't print monthly or year-end statements, except for the Fidelity 1099 that goes into the tax folder. In fact, I don't even look at monthly or year-end statements. With real-time, online access to everything, they serve no purpose for me. Statements had a purpose before banks went online. That was the only chance you had to validate transactions and reconcile to your own real-time records, typically a check register.
On the rare occasion that I need a statement for a real estate transaction or something similar, Fidelity keeps 10 years worth online that can be easily downloaded and printed. I monitor all our accounts including credit cards on an almost-daily basis. It's incredibly easy because almost everything is at Fidelity, and the two accounts that aren't, are on Full-View. So just one log-in to see everything. I've operated this way since around 2002.
All our bills are electronic (no mail) with the exception of the credit card accounts. For various reasons, I still haven't converted these to electronic or auto-pay. I keep about 6 months worth of CC statements in a file and shred the others. I keep 7 years of tax returns and supporting documents. All others are shredded. We have a printed Word document that describes all of our accounts and lots of other details to help the kids once we're gone or incapacitated. It's kept along with our important papers in a firebox. Both kids know where these papers are.