I view anarchism as a philosophy and lifestyle more than a government or system. Whenever you thwart, resist or defy authority, you are engaging in anarchism. This can’t be a system because it is a negative. It’s a response to power. What you are asking for is egalitarianism, and there are many kinds of egalitarian governance structures that have varying degrees of success. Ostensibly, the US is egalitarian. In practice, not so much.