Capitalism by itself does not produce egalitarian wealthy society. The system divides the populace into "capital owners" and "workers" who are in direct conflict.
There are plenty of capitalistic countries where most people are poor. In fact many of the as said Western countries has also high levels of poverty while running capitalism in the 1800 etc until post WW2 social democratic movements.
Once you dismantle those social democratic constructs such as labor unions and start shifting more power to the capital holders you'll see how the society splits apart to rich and poor. The rich use their wealth and power to rig the system to benefit themselves even more and become richer at the expense of everyone else. Ultimately they will remove democracy because functional real democracy is a threat to their wealth.