Memes

we need to abolish private property so everybody has equal power.

Abolishing private property isn't about equalizing power, necessarily. It's to end Capitalist production, which is necessarily exploitative and results in Monopoly Capitalism, aka Imperialism. Abolishing Private Property allows us to produce based on needs, not profits for a few individuals.

we class of people to maintain public ownership

Communists advocate for the abolition of classes.

After all, how can we enforce public ownership without a more powerful class of enforcers?

That's a pretty terrible misreading of Communist structures. Communists advocate for abolition of the State, via creating a government as an "administration of things," similar to how the Post Office functions, but for all of production. The goal of protecting the revolution is done by the Proletariat, the most advanced among them making up the Vanguard. There isn't a separate "class."