Ceteris paribus, they do (and certainly inequality has gotten worse in the US since Reagan's tax burden shift reduced tax progressivity), but particularly progressive tax systems are often pared with spending systems with less downward redistribution (or more upward redistribution) than those they are compared with, which counteracts the effect of greater tax progressivity; the US has less downward-redistributive spending than many other developed-world systems. [0] And obviously the tax system alone has less impact on inequality the smaller share of the economy taxation represents, and while the US tax system may be unuusally progressive, but it is also unusually light for the developed world (representing, at all levels of government, about 1/4 of GDP, compared to the OECD average of around 1/3.) [1]
OTOH, the people pushing for more progressive taxes in the US today aren't pushing for that alone, they are pushing for more downwardly-redistributive spending funded by the taxes, as well, and mostly also for taxes representing a greater total share of the economy, as well.
[0] https://www.economist.com/united-states/2017/11/23/american-...
[1] https://www.taxpolicycenter.org/briefing-book/how-do-us-taxe...