Even formal Anarchists struggle with this. In Act 1 of the Mexican Revolution, while denouncing all political parties as corrupt and puppets of the state or the elites, the first effort of the movement--after starting soon-suppressed newspapers--was to create the Partido Liberal Mexicano.
Yes, King Sobhuza II of swaziland introduced the Tinkhundla monarchical system which negated multypartyism on grounds that it was divisive and un-African.
When people are prevented from coming together to create power through organizing, as would result from the prohibition of political parties, it is in effect giving control over to that society's elite who control existing resources.
Many local governments in the United States and Canada prohibit placing a party identification on the ballot along with the name of a candidate. Non-partisan elections are a long way from prohibiting the organization of political parties, of course.