People with lower incomes have a lower savings rate because they have to buy essentials, yes. Wealthy people would then end up paying a much smaller percentage

People with lower incomes have a lower savings rate because they have to buy essentials, yes. Wealthy people would then end up paying a much smaller percentage of their income compared to everyone else. People who come into wealth quickly seem to spend money quickly (athletes and lotto winners come to mind, hell even Willie Nelson went bankrupt at one point). People who earn wealth more slowly tend to end up investing their money and saving a larger percentage. If you make 300k/year, you could save 25% without blinking an eye, not so much if you earn 30k/year, especially if you have a dependent.