I personally think that the social network is not owned by any one person or entity, keeping it from being subject to corporate take-overs or advertising. In September 2011 the developers stated, "...our distributed design means no big corporation will ever control Diaspora. Diaspora* will never sell your social life to advertisers, and you won’t have to conform to someone’s arbitrary rules or look over your shoulder before you speak.
No, the other social networking services are too diverse for one application to replace all of them. The differing functions of Twitter and Facebook, for example, require two different types of interface to work efficiently. Facebook is working to remain ahead of the curve in terms of adding WhatsApp to its holdings and making voice chat possible.
Looking at joindiaspora.com and diasporafoundation.org I believe they have a service that is unique and it addresses some of the privacy issues people are concerned with today, but they don't have the following. That is the major problem and it doesn't look like they're trying to address it, so it is unlikely that they will replace other social networking services at this time.
Diaspora is poorly marketed because it does not believe in advertising. It is a free, open source service. This makes it easily accessible and much more appealing without the constant bombardment of advertisements. People don't care about that though. People care about popularity and marketing of a product. How efficient it is matters only to a few.
No, Disapora will not replace other social networking services, because it has not gotten any traction at all. Social networking systems only work if the people who have them want to use them. They don't have much of value, other than word of mouth and a good reputation. Disapora doesn't have that. So they will not overtake others.