A couple of thoughts on this, Andrew. In Hebrews, Jesus is presented both as example to follow in his suffering (Hebrews 12:2-4), and as atoning sacrifice and inaugurator of the new covenant in our hearts (Hebrews 9:12-15; 10:1-22). There is a greater emphasis on the latter than the former in Hebrews, though from your perspective, it is still arguable that this is what God did for Israel historically, rather than for humanity universally.
So how is it that Hebrews, along with most of the New Testament and Jesus’s actions in particular, has been interpreted as applicable to humanity generally, rather than a story in history which facilitated benefits to humanity, but not directly?
First, because that is how humanity has experienced it, that by believing in Jesus, and in his death as atonement for sins in particular, it is our sins he died for, and by his resurrection and ascension, new life through the Spirit is received from him.
Second, because the wider story at work in the background of the scriptures bears this interpretation out - that Jesus came to bring the story of creation, fall, redemption and new creation to its climax. The passover meal he celebrated with his disciples before his crucifixion enacted the fulfilment of the Exodus as a story in search of a conclusion - in himself. The Exodus was a story within a story - the story of Abraham, with the Exodus as a springboard to entry into Canaan - Genesis 15.
Looking back from Genesis 15, The story of Abraham was couched within a story of creation, fall and universal sin - Genesis 1-11. Looking forward, the entry into Canaan was a springboard for God’s universal intentions achieved through Jesus, Abraham’s seed, and seed as all those who believed in Jesus.
Much of Hebrews is describing the fulfilment of the OT sacrificial system in Jesus, just as the passover meal he took with his disciples was an enactment of that fulfilment. The difference of emphasis that a narrative interpretation brings to Hebrews is that instead of seeing Hebrews as an invitation to complex typological interpretation of the OT temple and sacrificial system, we can see it as a fulfiment of a story which was winding its way to a conclusion, not, as expected, in the nation of Israel, but in a representative of that nation, through whom the nation’s destiny, to bring blessing to the world, would be fulfilled.
I know that discretion should be the better part of valour with these posts, but here I go again putting my head into the lion’s den (or something).