Inflation helped you to escape poverty by reducing the purchasing power of other people's wealth so that you could catch up.
Warren Buffet literally describes inflation as a tax - I agree with that. Taxes are [should be] a way of redistributing wealth more fairly.
Responding to your later edit: yes, wealthy people have more opportunities that come from wealth, and therefore can expect their wealth to collect more wealth disproportionately quickly. Inflation does work to correct this.
A legal change to make minimum wage track inflation and dramatically increase (double?) the currently unlivable federal minimum wage would also be helpful though, as would restoring workers' rights (especially collective bargaining rights) which have been gradually but systematically eroded for the past 40 years.