I guess by "the left" you mean Democrats? They're mostly liberals, not leftists, and want to maintain the hierarchies but ease some of the most obvious impacts through regulations.
The idea that "left means more government" is also very ahistorical and feels uniquely like a product of modern American political discourse. The origin of the left-right distinction is literally the abolition of feudalism, i.e. replacing a fixed hierarchy by birthright with egalitarian democratic elections. By 1776 standards the founding fathers were left-wing radicals. The right would have literally defended the Crown.
If you understand left-right as Democrat-Republican, your view doesn't hold true either. Republicans generally want to void labor protections, reduce taxes, cut social welfare and lift environmental regulations, but they also always want to increase the military, intelligence and police budgets. Republicans also tend to want the state to enforce their idea of morality, e.g. by prohibiting (secular or non-Christian) same-sex marriages, criminalizing abortion or restricting sex education and access to contraceptives. They want to enforce what they see as the natural order through punishment whereas "the left" wants to counteract it through support. Prison abolitionists tend to be on the left, not the right.
The government isn't hierarchy. The government is an institution that interacts with hierarchy. As are large corporations for that matter. Reducing the government budget and shifting more economic power to corporations doesn't reduce hierarchies, it only takes power from elected officials to unelected shareholders.
If you believe in an unregulated free market capitalism, you literally support the hierarchy of the market and you believe in a natural order. Or to put it in words that feel less icky if you think of yourself as an anarcho-capitalist: that people should vote with their dollars on what goods and services should thrive or fail.
If you believe money is power and you believe it's good and natural for some people to have many orders of magnitude more money than other people, you believe in a natural order. This is what leftists call a hierarchy and leftists don't like it.
Note: I'm not saying leftists don't want a big government. I'm saying leftists (even outside anarchism) want to get rid of the state. They just disagree on how to get there. And for reformists that answer usually involves using the state one way or another.