"Bitcoins are implemented on a massive scale, then there is a heavy chance that the rich will no longer become richer and the poor will no longer become poorer"
This is how we know you are not being realistic. Bitcoin is not pixie dust.
Let's put it this way: rich people could just buy all the Bitcoin currency units out there with their other assets, and then you would see them become even wealthier just by holding on to those units as deflationary trends kick in, and that is assuming that we lived in a universe where currencies without any legal structure around them can really become big. Do you really think people are going to forget about US Dollars or Euros or Pounds Sterling overnight? People still need to pay taxes, they still have to use courts to settle disputes, and so forth -- and poor people are going to be in much greater need of the currencies used for those things than rich people, and will be much more willing to exchange Bitcoins for those currencies.