John Day, author of the Real Life Accounting online course:
Good reason number one: A manually prepared bank reconciliation forces you to familiarize yourself with the deposits, checks, bank charges, outstanding checks, outstanding deposits, mistakes, bank errors, and other strange phenomenon that occur occasionally during a month's bookkeeping transactions. This information that gets assimilated in your brain is invaluable when problem-solving later on.
Good reason number two: All the information regarding increases and decreases to your bank account are right there on one page. You will require this information when writing journal entries to make sure you have captured "all" the transactions that have occurred during the month, related to cash.
Good reason number three: The completed bank reconciliation form is a great reference for you when trying to figure out why your Cash account is out of balance. Theoretically, your Cash account should be in-balance. However, for some strange reason, this often is not the case.
Good reason number four: Keeping your eye out for outstanding checks that never clear the bank (stale-dated checks). Sometimes a check is voided but doesn't get removed from the register. Sometimes a check gets written but doesn't get put on the register but then clears the bank. These items require special adjusting journal entries. You can't write them if you don't even know about them.