I write in non-linear sometimes. It's definitely something you have to do right - and goodness knows I've gotten it wrong at times.
But I like reading it when it's done well. For some reason it feels more real to me. In reality, although we go through time linearly, we don't really experience our lives that way. There's throw-backs and lessons learned and applying that to whatever you're doing now. And that winds up having the effect of non-linearity through life. At least it does to me, but maybe I'm just crazy.