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IIRC they can report for 7 years. Inactive accounts will report -- they don't immediately fall off. You can attempt to get them removed with a goodwill letter to the creditor but the creditor doesn't have to do anything if the information is valid.
Any procedure that would provide consumers the ability to remove derogatory information on their own would be contrary to the intent of the credit reporting system, which is to provide others an accurate history upon which to base their decisions.
Ergo, the reason for the CRA policy that instructs furnishers not to subjectively delete accurate reporting based on subsequent payment of the debt.
They want their CRs to be complete, and thus of the most value to their customers.
Asking the creditor to voluntarily delete adverse information, or the entire account, requires no reasons provided to the CRAs should they agree to do so, and thus is available, but not generally considered to be in the best interest of the system.