The main thing they are trying to play on is being a censorship free place for people instead of something like facebook, twitter, or YouTube where you can be kicked off or buried for saying things that aren't politically correct.   

The thing I would say about having your own blog on your own website is that it is very hard to get enough traffic to make it worth anything.   Even a guy like Jerry Banfield who has a very solid audience only makes a couple of dollars / month from Adsense on his website and he has been building it for a couple of years.   You can get so much more traffic where the people already are.   I posted a couple of those small posts and I got 18 views on one of my posts.   That isn't a lot but it is way more than a person would get in the first hour of having their own website and trying to monetize it.  Personally what I have found out over the years is that a lot of these people stick to consuming content mainly on the big platforms and the hope is to pull them away to buy some merchandise or to purchase a program on your own website.   

The greatest advantage to Minds is that it seems to be free thinking liberty minded type people and if a person has a topic that relates to that type of thing like cryto currencies then a persons fan base could grow from being on there.    

But to be honest from what  have seen the best way to play minds is to create the account to secure your user name and then it lets you link Facebook and Twitter accounts so you can just have it repost all the stuff you put on those platforms.   That way you don't really have to manage Minds unless it became a bigger thing and then the focus turned to it or something.