Morality was the main factor in my decision to stop drinking because of the harm I was doing to myself and others. This does fit in with all the world religions quite well because they all counsel self-control and warn against hedonistic pleasure and so can provide the initial motivation to stop.
I needed an absolute, cast-iron guaranteed way to stop drinking which ultimately meant that I had to rely on my myself. and relying on any external help would have meant an indirection and dependence that would not have worked for me. But I think this is still compatible with mainstream religions because, in their best representations, they all talk about taking self-responsibility for our own actions. I agree with you though that religion is often portrayed in ways that detracts from personal responsibility as if it were something that's old-fashioned and of no contemporary value.