Rather than claiming that the law failed, the author of Hebrews claims quite the opposite throughout the work. Consider Hebrews 9.13–14 (cited by Ellingworth). The author says: 

For if the blood of goats and bulls and the ashes of a red heifer sprinkled on those defiled consecrates (ἁγιάζει) for the purification of the flesh, then how much more will the blood of Christ, who offered himself blameless to God through the eternal Spirit, cleanse our conscience (καθαριεῖ τὴν συνείδησιν ἡμῶν)…? 

The author uses an argument from lesser to greater here, and that argument depends upon the effectiveness of the Levitical offerings (Moffitt 2019). The blood of goats and bulls and the ashes of a red heifer consecrate; that is a claim clearly made. Those items cannot cleanse the conscience, but they were not intended to do so. - Madison N. Pierce, Relapsing, Reverting, or Rejecting? The Purpose of Hebrews and Early Jewish Religion