I closed my checking account, but the bank continued to accept the recurring charges from my insurance company. Why doesn't the bank reject these charges?

Generally, it is your responsibility to cancel all recurring charges with a third-party before closing an account.

The original agreement to charge the account was made between you, as the accountholder, and the merchant. You probably provided the merchant with written authorization to debit your account. Because the bank was not a party to that agreement, they cannot cancel it for you. You need to instruct the merchant to cease debiting your account before closing it.