We went through a spate, a few years ago, of scanning and shredding all our old bank statements - that’s a fair compromise between keeping the paper and getting rid of it all.
Now, we download and store all the statements each month. It’s all up on our Dropbox, with folders for each account and year. Odds are we’ll never need it but better safe than sorry.
I recently needed to obtain statements and canceled checks from an account that was closed in 2014. I had to go to the bank but it wasn’t a problem, I was able to get everything I needed.
It was a little difficult in my case, but that is because I needed the information from my mother’s account. She is incapacitated and I was handling some legal issues for her, remotely from another state. I am listed as power of attorney on her current accounts but not on the account that was closed in 2014. So my bankers had to go through several layers of legal approval, but they had no issues getting to the account information.
When I needed one last document from the long closed account, I was visiting Mom and was able to go to my hometown bank where they know me. That transaction only took 30 seconds.