Wealth inequality rises by default as rich people are able to invest more of their income than the average working person who is forced to spend a greater percentage of their income on consumption just to survive and live.
I disagree. Any inequality is the result of unfair laws. For example in countries with liberal economy and capitalism such as United States the ultra rich have the power to lobby behind the scenes and pass laws that help them not pay any taxes. This and a lot more unfair laws help them amass wealth while the lower classes are milked out of their last cent in form of taxes, interest rate, etc.
One way governments have tried to cure this imbalance (and win elections) is through running fiscal deficits in order to fund massive social welfare programs, healthcare programs, education programs and infrastructure projects amongst other things.
That's like trying to fix a broken leg by taking a pain killer!
These things are like pain killers, they "hide the pain" for a little while without fixing the actual problem at the root. The problem I explained above.
As the world transitions to Bitcoin,
That is not happening and is not supposed to happen.
Bitcoin is and will remain an extra payment option with unique features.
It will not replace anything and the world will not "transition to bitcoin".