First, income inequality doesn't measure income mobility. Places like the US that have a huge number of unskilled illegal and legal immigrants constantly entering at the bottom level will always have high income inequality. The question is, what happens to each individual over the course of their lives?
83% of Americans will earn more than their parents. 73% of Americans will spend at least 1 year in the top 20% of income earners in their lifetime.
https://fee.org/articles/income-mobility-data-show-america-s...
Also, there is no such thing as "trickle down economics", that is an insult leveled by critics of the idea you should let people spend and invest their own money rather than the government. The results speak for themselves and are astounding. The poorest person alive in a first world country today lives better than the richest 100 years ago. This was all because of investment. Clearly investment, or "trickling down" (as its critics like to call it) isn't just effective, it is the only thing that works to make people's lives better.