There's a whole book about 4:33, its origins, its formulation, and its aftermath. that is quite illuminating: No Such Thing as Silence: John Cage's 4'33" (Icons of America): Gann, Kyle: 9780300171297: Amazon.com: Books
Highly recommended.
Bottom line - with 4'33", Cage was very much about everybody paying attention, not just to one thing at a time, but everything all the time.
One of the more penetrating insights from this is that "composition" is essentially an imposed, discovered construct based on the limitations of the hearer. The more open our ears/minds, the more "composition" we "discover" ("discover" being a misnomer, because how do you discover something that's already there?)
It's a bit of vanity, really, to imagine that we "discover" or "create" music. All sound is always there, somewhere, past, present, and future. All we do is process it as we find it. Nothing more than that.
Now, for the sake of reductive conversation, we label certain things "music" because we don't know any different (or jsut don't want to work that hard at any given point). But if something would be considered "just sound" (or even NOISE) in the 18th Century but is accepted as "music here in the 21st, what has changed? The sound itself? I don't think so. It's the individual and collective awareness and acceptance.
So yes - all sound is POTENTIALLY music, and it's not necessarily a "composer" who can make it so. It is ANYBODY'S prerogative and privilege to do so. Ultimately, we are our own composer. "Organization" is what we make it to be. Ot let it to be.
That may or may not be a "rabbit hole", but I've found it to be more of a thought that once engaged cannot be unthought.
Or more to the point - yes, "music" is indeed "organized sound".
But - whose "organization"? What organization? And if we don't sense it, does that mean it's not there?