[WS:] I think it is far more than just providing high moral grounds. Social solidarity is what some sociologists call 'social capital' - a resource that can be very valuable for organizing. I believe, but I cannot prove at the moment, that the waning of "traditional" mass movements is linked to loosening of social solidarity ties by capitalist development, especially suburbanization. It may be easier to call people to show up for a demo using the internet, but it is rather difficult to keep them involved if they are not already connected by social solidarity ties.
This issue has been extensively discussed in social movement literature. To summarize, social movement are high risk activities with low payoff, which means that participation carries considerable risk and cost to individuals, but the payoff of that participation is first uncertain and second constitutes a "public good" i.e. everyone will get whether one participated or not. For that reason, social movement participation is not "rational" and thus difficult to maintain. However, social solidarity ties can fundamentally alter this cost/benefit balance - it can reduce individual risk of participation by spreading on an entire community, it can provide social rewards (e.f. respect) for participation that go beyond "public goods" that a movements strive to achieve, and can be instrumental in mobilizing additional participants, which increases the chanced of the movement's success.
For that reason, I tend to be rather skeptical about the "social media" hype in social movements. It appears that all credits for organizing such movements is given to a few nerds with internet access so it appears as if they single-handedly "mobilized" these movements, whereas social solidarity ties that made it all possible are ignored.
Wojtek