Corbyn couldn't. As someone I read put it (damning with faint praise) and I paraphrase, "if Corbyn doesn't have authenticity, what does he have?" But no-one else needs to be burdened by the awkwardness of his backhistory.
Blairism is dead, so much is clear. Momentum was something that can't be undone, and even if centre-inclined pragmatists have been restored to control of the Labour Party, Momentum have indelibly shifted the tone to the left; the most Blairite centreists quit the party and promptly disappeared in ignominy. Labour was in a sense successful even despite losing the election: Johnson at least nominally committed to massive infrastructure and social spending, as a clear indication the Tories knew Corbyn's Labour was scoring some major victories in the policy argument. Of course, he'll try not to do actually do it because his cabinet's full of ultra-capitalists, but if the language has shifted leftwards, policy is likely to eventially follow: the Tories deliver or risk failure.
Brexit was an utter failure for Labour. I think they could have survived Corbyn alone, or Brexit alone, but not both. Labour's response to Brexit was in many ways as weak as the Tories, except without the visibility of being in government to see it played out so vividly in the press. But they had a perceived weak leader who seemed to be fudging the biggest issue of the day.
As for the Labour Party infrastructure, shit. A friend of mine used to be heavily involved with Welsh Labour. Years ago, the party in Wales realised how thin the loyalty of lots of voters was and took measures to deal with it. In Scotland, they remained flabby and complacent, and were duly wiped out the minute they faced a major challenge. In lots of parts of England, the local parties are complacent and toxic, and they've taken the support of too many voters for granted.
If there is one thing that amazes me about Blair and Blarists, they seem to amazingly blind to how they've eroded and disillusioned many people's support for their own party, and don't seem to realise its 2020, not 2000, and that 2000 stuff just won't fly any more.