Blockchain and Inequality
Blockchain won't as it is the software that is really more enterprise software at the core. Blockchain itself may have a helping hand by helping Real Estate titles not be changed by dictators for example, but mostly its a shared ledger for companies.
Cyber currencies , based on Blockchain tech, will either be a great liberator of common people helping to narrow the inequality gap (If you listen to coin enthusiasts) or help make the gap wider. I believe if you understand that 100 people own 40% of all Bitcoin and 12 own over half of IOTA, etc. you can see more power growing in the hands of a few. Until cybercurrencies get restored to what Satoshi wanted, I think they will widen the gap. (IMHO)
Blockchain technology if implemented in the areas which matters to individuals e.g. government benefit distribution, claims settlement, land registry, etc. would provide a much need transparency and tracking of funds / assets / benefits. This would reduce middle men, corruption and in a way provides opportunity for upbringing of under privilege people.
However, reducing inequality has less to do with a technology but it is more on the willingness of the people in power to make attempt to do it. This can still be achieved with other techs and rules implementations if required to be done. Blockchain kind of make it relatively simpler I should say.
I think there will always be an inequality gap.
Look at the Internet. In the beginning it was announced as giving access to information to everyone FOR FREE - with hotspots making things pass smoothly.
Just looking to the access item, there are big differences between "rich" countries and "poor" countries and even inside a country, there is a large inequality. In cities, you have 4G networks giving mobile access to the internet but one you go out of the cities... it starts getting difficult. At work, I have 4G but at home, I only have 2G (so I don't use mobile internet).
Blockchain will be the same - large companies have the ressources to take benefits from it while small companies will be followers. There could be some disruptors but there will always be an inequality gap.