Free market capitalism doesn't pander to the rich. It allows the economy to function in an orderly fashion which allows people to trade labor and goods freely. To 'pander' implies that there is some outside agent acting on the economy, therefore when the rich are 'pandered' to, you don't have a free market.
Trickle down economics has a history of working. When America and Britain had very close to free markets, the standard of living of most men grew by leaps and bounds. The average life expectancy increased, population increased, and opportunities for social mobility increased.
Your observation regarding high tax rates leading to progress are incorrect. Americas greatest economic booms follow deceases in tax rates. For instance Americas greatest economic boom happened in the late 40's and 50's when the tax rate was rolled back. America has one of the three highest corporate tax rates in the world. If your theory regarding tax rates resulting in productivity are true, why is America a net import country with high unemployment shedding jobs? Shouldn't the economy be booming and industry expanding? Ever her of The Industrial Revolution? There was an effective zero percent tax rate during this time. The government supported itself primarily on tariffs and fees. Are you going to assert that The Industrial Revolution wasn't one of the most economically productive eras in history?
You keep mentioning corporations, but corporations as you talk about them are not the product of free market capitalism. Corporations can't exist in free market capitalism because corporations are legal entities created and enforced by the government. Corporations are legal shells that shield the members from criminal and civil responsibility for their actions. That means the government is tampering with the economy to maintain corporation, hence no free market.
"Trickle down" isn't an "experiment". It is an emergent order that occurs when wealth is produced. In order to expand wealth, the entrepreneur must create more jobs and industries. This expansion benefits booth the entrepreneur, the employee, and the consumer.
The economy is over regulated. It's extremely difficult and expensive to start a business in America. This means only the very well financed (rich) can start a business. Your beloved regulations therefore in part cause the problems you are attributing to the free market. I witnessed my father close the doors of his business due to over regulation. He hit economic hard times and no longer wanted to deal with government regulations such as unemployment insurance, workers comp, OSHA fines, etc. Your beloved regulations were instrumental in my father shutting down his 41 year old business and the ensuing layoff of 75 full time employees.