In the world, the wealthy become wealthier, the poor become poorer, the middle class disappears. One of the reasons of this is the inflation: it is a kind of regressive tax, this tax is paid mostly by the poor because they loose their savings, while the wealthy keep their savings not in money but in assets. So, since the bitcoins are a way of keeping the savings, they can fight inequality to some aspect.
However, I am sure that only switching from inflational economics model to deflational one can't change the things significantly. The main reason of the disappearance of the middle class is political: the wealthy 1% of the population are the ruling class, and they pass laws for making them more and more rich, for example under Reagan the taxes for wealthy were cut. They also control the mass media like CNN or Fox News, and these mass media lie about the problem of the disappearance of the middle class.
But I think that the rise of cryptocurrencies will be an important first step towards a revolution in the Western world against the Deep State. I found that many people in the Western world, especially in Europe, are brainwashed - they often simply deny that the inflation is a hidden taxation. So when the bitcoin will cost 1m, these lies of the ruling class will be destroyed, the people will start thinking. That's why buying bitcoins now is an investment into future revolution of the Western people against the Deep State, so I think that in nearest years the bitcoins will grow very rapidly.
Why do you say that the middle class disappears? They don't disappear; they become poor and then go into the poor category because they can't keep up with their current class due to high inflation and low wages. Also, maybe you are not aware of it, but even Bitcoin and cryptocurrencies are regulated and taxed in countries where they are legalized and bills are passed for them to be used by the general public, but they will be regulated, and people will be taxed based on their assets. Even though there can be ways to stay anonymous, but most people won't do it because they don't know, they will use centralized platforms with their personal identities and then pay taxes for even owning cryptocurrencies.
The theory about the rich getting richer and the poor getting poorer is basically something that I don't condemn because growing up, I learned that it's not the fault of the wealthy that they are able to make more money because they are capable of it, they have money, and money can help you make more money. If I'm poor, and I can't make my financial life better for any reason, it's my fault, and the fault of my ancestors because they didn't work hard enough to take us out of this condition, and it could partly be the fault of the government for not providing us with proper education without costs so that we could at least do something for ourselves when we grow up.