The works principle enunciated in Lev 18:5 included the ceremonial law & sacrifices (Num. 3:10; Lev 8:35; 10:2, 7, 9; Ex. 28:35, 43; 30:20-21, etc).
‘Thus you shall separate the children of Israel from their [ceremonial] uncleanness, lest they die in their [ceremonial] uncleanness when they defile My tabernacle that is among them." (Lev 15:31)
In this sense Heb 9:13 teaches that animal sacrifices were actually efficacious for their purpose. They could ceremonially cleanse an Israelite and thereby save his life. But it could not do so eternally, nor could it cleanse his conscience - only his flesh.
