Is there any reason to keep expired passports? Is shredding a good way to get rid of them?
Other than nostalgia, no, no great reason to keep them. Seems an expired ID gets you nowhere these days.
You can shred them if you wish, some places have secure disposal (that goes to a shredder), or toss them in the trash. There really is no confidential information on a passport, but many feel better to be safe.