Perhaps, but not necessarily, Venezuela and Vietnam both have lower government spending per GDP than the USA, and neither of them are exactly capitalist paradises. But ... you have to ask about the chicken and the egg then. if high spending nations in Europe have the lowest inequality compared to low-taxing nations, then perhaps the lack of a strong government spending sector drives higher inequality.
In fact, if you look at the countries with lower government spending per GDP than the USA
on this comprehensive list then there are basically zero examples of the libertarian dreamland to be found. The only exceptions are a few city-states that effectively attract tax dodgers from larger nations, and the "city-state leeching off larger nations" model is something that clearly doesn't scale up.
e.g. Mexico's government only spends 24% of GDP vs 38% GDP in the USA. And just think about that. Mexico is the #1 nation likely to benefit from lower taxes because of American businesses right next door looking to save a buck on their taxes. Yet the lower taxes/spending in Mexico haven't help even with that advantage. How is lowering taxes going to help America when there isn't even a bigger America next door to attract investment from, when lower taxes clearly haven't helped Mexico in the first place?
Taxes get spend on roads, public transport and infrastructure. Think about the extra costs you'd have setting up a business in a place where those things don't exist. Both customers and employees can get to a business much more easily when there's subsidized transportation. If you set up a factory in a place where your employees absolutely 100% must own a car to get to your business, do ya think you could attract
anyone to work for minimum wage, let alone less than minimum wage? And how are your customers getting to your location?
Companies that are paying minimum wage right now
absolutely are only able to get away with that because they are being subsidized by the huge public infrastructure spending that exist in the USA. If they had to pay the true costs of getting both workers and customers to their locations, then they would go out of business, and minimum wage workers are often still receiving some sort of welfare payments. So ... it's arguable that current minimum wage job providers are leeching off social spending.
And the problem with saying e.g. just have private bus companies to take up the slack, is that a private bus company must make all their money from that one bus route, so they can't take externalities into account, e.g. the value of commerce created because the buses were cheaper. A public bus company can take into account the holistic situation. If bus fare prices are cut in half, more people will travel and they will spend money in local businesses, which creates new sources of revenue, which can then pay the costs of the buses. When everything is private and disjointed, those types of synergies can't happen.