You mean the Jack Kerouac who ended up drinking himself to death? Perhaps the road trips did not cure all ails.
Kerouac himself was smart-enough to realize the dynamic and illusory nature of what we call "myself" (it was one of his main themes - unfolding of Cody and himself and of everything else) and that his alcoholism was the cause of his suffering.
Why he didn't choose to fight it is another question. Perhaps, it was too late.