What does it even mean "one less account to track?" The money is still coming from a bank account, if you track the money in your account you would still have to account for a check, and it would be even worse if the check isn't cashed right away.

Is it that you don't have the monthly credit card bill if you send a check? But you're spending the same amount of money regardless, checks are more like one-off credit card transactions, that don't confirm payment like a credit card does. Checks are worse for the payment-neurotic. That's maybe an argument for debit cards, it's not an argument for checks.