Honestly as someone who has been trying and failing for roughly my entire life to complete a worthwhile novel, I think not following structure can hurt you. I don't like structure, I don't like most main plot conventions or the huge need for a left-field twist at the end or massive amounts of seemingly manufactured drama as well, and much prefer writing developed characters with interesting relationships who grow and change in a manner that feels real, which usually isn't easily divided into 3 acts. Still, what I get when I ignore all these things is a meandering mess of a story that is way too slow of a burn for even the most patient of people and just feels like characters flowing from one self-contained event to the other.

I think if you want to keep away from these trends the best mediums to do it with would be something like comics or a t.v series which don't need to so neatly fit an entire story and its arcs into such a limited amount of space, and don't have the expectations of that happening each issue/episode. Unfortunately unless you can draw as well as you can write, or have connections, you probably don't have the option to utilize said mediums.

So basically what I'm trying to say in a rambling sort of way is that the best writing ignores these things, but most of us aren't the best writers.