For your example, to make the list clearer in writing I would usually do one of the two.

I like Jazz, Rock and Roll, and Classical.

Or

I like Jazz, Rock & Roll and Classical.

(Or the other way around if a list item includes "and" specifically)

I often write in a way that flows better when talking, so I usually try to find ways like the above to make that kind of flow look more understandable in writing too. I don't think your and-less version flows well, in my way of speaking at least. But I also wouldn't tell you to stop doing that, because I can understand it, and that matters most in reality.