You will notice that the guy in the video mentions the phrase "the rich get richer" when discussing POW at 5:10. This is a common put down when discussing POS. Although this is true, it gives people the wrong impression and guides them to the wrong conclusion. This is my attempt to explain why.
MAKING MONEY
A shovel simply can't do the work that a giant bulldozer can. If you're hiring yourself out, generally you're going to get paid more if you're hiring yourself out with a bulldozer than a shovel. Why? Because you can do more work with a bulldozer. This situation is simply a fact of life and it's based on basic logic, economics and physics. The guy with the bulldozer must have a certain amount of wealth to buy it. You can see that wealth allows people to make investments that will then allow them to make more wealth. This is an issue that we face on a species level, not just something that is limited to the world of digging, or Cryptocurrency. Many countries have tax systems that try (or appear to try) to balance this effect out.
MINING - POW
Consider the previous situation, but now let's apply it to mining. Now the everyday guy with the shovel is the guy with a basic GPU mining rig and the guy with the bulldozer has a state of the art warehouse full of Application Specific Integrated Circuits (ASIC), cheaper electricity, more efficient hardware, and an internet connection you would die for. This creates a dangerous feedback loop. With more resources you can generate more money, which you can then invest in research/developing better technology which leads to more money! What is really scary about this situation is that the intellectual property used in the hardware can be kept from the people with less wealth. This factor accelerates the growth of the wealthy to the point where everyone else drops out and one entity has a complete monopoly on mining. Another thing that is worrying is that there is no way to know if one entity is actually controlling multiple mining pools and has taken control of 51% of the networks hash rate. POW is a good system, and I'm not saying the previous situation has happened, but it's important to be aware of the economics and logistics. It's important to note that if it was found out that one entity had control of 51% of the hash rate, then it would instantly make the whole system worthless, and hence the entity's business and Cryptocurrency in the system. The point is, there is an inbuilt incentive to not get too powerful that can be applied to both POW and POS.
POW - RICHIE RICH GET'S RICHER LESS
So why do I think the rich get richer less with POW? With mining the super wealthy can invest in research and produce expensive machines (etc) that give them an ever increasing advantage over average Joe. That can't be done with POS. There are no ASICS. You can't invest in better staking technology. You can't price others out of staking. The inbuilt 51% economic safety mechanism still applies to POS, but now the super wealthy can't price average Joe out of the system and he can work his way up to financial freedom. It's 'shovel vs bigger shovel' rather than 'shovel vs bulldozer'.