Except people are not automatons who have a single set of desires and, once they've fulfilled them, are content and don't want anything else. People's values and goals change over time, creating new wants and needs which they will pursue. For most things in life, the only kind of happiness is momentary happiness. It's very rare that you have a desire that can be filled by doing or acquiring a single thing.

Eliminating material possessions sounds like an awful idea. Whatever "true happiness" is probably varies from person to person.