Inevitably in any group someone will emerge as the central organizer. I think the idea is that it should allow to happen naturally.
If truly no one is able to get a team organized I’d say treat it as an exception rather than a rule and figure out what is hold the team back from being more organized
Sure, someone will emerge. I've seen that scenario happen over and over. Will the result be good? No, not in a single case i observed because managing a software product is a distinct art which too many software developers believe goes naturally hand-in-hand with their coding skills.
Team organization isn't the same thing as managing a product. Self organization is about teams having autonomy to organize and plan units of work and drive the teams forward. This isn't some magical vacuum where the business has no input on what those things are, and you very likely should have some distinct product management that engineers aren't in charge of.
If truly no one is able to get a team organized I’d say treat it as an exception rather than a rule and figure out what is hold the team back from being more organized