There is a trickle-down effect, but it's not nearly as strong as some people think.
You can think of progressive taxes as a form of insurance policy on the misallocation of resources by wealthy people. Wealthy people may on average make better resource allocation decisions, but sometimes there are mistakes. Progressive taxes prevent wealthy people from gaining so much that a single mistake will be catastrophic.
The mechanism by which the free market performs better than a command economy is that of distributed decisions. Instead of a central planner, everyone makes resource allocation decisions based on price information. This free market mechanism works to the extent that resources are distributed. Thus progressive taxes ensure the continuing efficiency of the market.
You can think of progressive taxes as a form of insurance policy on the misallocation of resources by wealthy people. Wealthy people may on average make better resource allocation decisions, but sometimes there are mistakes. Progressive taxes prevent wealthy people from gaining so much that a single mistake will be catastrophic.
The mechanism by which the free market performs better than a command economy is that of distributed decisions. Instead of a central planner, everyone makes resource allocation decisions based on price information. This free market mechanism works to the extent that resources are distributed. Thus progressive taxes ensure the continuing efficiency of the market.