Self-publishing means handling all registration, collection, and exploitation yourself. It works when you have limited commercial activity, write mainly for your own artist project, have time and inclination for administration, want to learn the business before committing, or value complete control over limited income.
The breaking point usually comes when administration time interferes with creative work, international usage increases complexity, sync opportunities require industry relationships, or you discover money you've been missing. Most professional writers eventually need at least administration support. The question becomes not whether to work with a publisher, but what level of support you need. Starting self-published can be educational, but don't let pride or misunderstanding of publisher value leave money uncollected.
