People forget their PINs etc.
I know one person who lost out on a refi as they couldnt unfreeze for about a week.
But for you, it is a good idea. People should consider it.
Agree with what everyone is saying. Shredding probably has more value as peace of mind rather than preventing ID theft.
How about credit cards? Or other plastic cards we may be carrying around (AAA, health insurance, etc.)? I always cut them up before throwing them away, but then I think that putting all the pieces in the same garbage bag would make it so someone would have an easy time putting the pieces together if they were so inclined. Not that it matters for an expired credit card. That risk is probably on the same level as shredded paper, I suppose.
If you have a decent home shredder it will eat plastic credit cards just fine.
For a couple years there was a fashion for prestige credit cards that were actually metal. Very heavy and substantial feeling; you knew you had clout (remember that ad series?) when you slapped that baby on a counter or clerk’s palm. Don’t try to shred those at home. It took me an hour to disassemble and unjam my shredder when I tried. 
The masking isn’t always very complete. For example the standard credit card bill hides the number. But the coupon that you’re supposed to include with your check? if you look carefully there’s a row of digits along the bottom that is OCRed when they process your check. Your complete CC number is probably in there in plain text. I have cards from most major issuers and it’s right there in plain well-known-to-criminals sight on each and every statement.
If you have a financial / brokerage account that includes a deposit slip with some or all statements to encourage you to send them funds, it’s quite likely the full account number is on there too.
There’s a counter argument to be made. Which is …
If I activate the online access feature for my account at Bank X, the bad guys then need to hack into my password, 2FA, etc., to get in. Provided I have a good long secure unique PW that can be a tall order.
But if I haven’t bothered to set that online access up yet, then it’s a virgin field for the bad guys to set up the online access to my account for themselves using their email address and password from the git-go. It’ll be a couple weeks before the bank sends a “congrats on your new online access” snail-mail letter to me. By which time the money may well be gone and/or the snail-mail address changed to be them. And I may well confuse that letter for marketing trying to convince me to sign up, rather than notice that “I” had signed up. Leaving the bad guys fully in control.
I’m not competent to really assess the relative merits of the two approaches in depth, but I have chosen to activate online access with solid PWs & 2FA where possible for everything. In my reckoning, better to be facing a known unknown than an unknown unknown.
I see your point, but when I did activate mine (then deactivated it, the bank gave a bonus for activating it) the bank sent me a immediate email.
This point is debated at Bank Security conferences. Both sides make a point. I choose to be conservative. Besides they needed my PIN also.
Ha ha you’re right. The payment coupon has my CC number in OCR text across the top, while the CC number below the “Amount paid” window is nicely masked in sans serif. .
This is probably overly paranoid, but when I cut up a card, I distribute the pieces across several garbage cans so they don’t all end up together in the trash.
When my card went to pieces (Literally. 5 pieces), the place I was staying wouldn’t accept it. So I took it to the bank and got cash…
Hahah- so do I!