It's an interesting idea, however the slow part of this social network doesn't make it built more for friends than an unrestricted network. It seems to solve the noise and lack of depth part, but that has just as much value outside of your close friends network. So I would focus the messaging around that part - slow and deep - rather than the friendship part.
And then there's the inherit issue of a restricted social network being disadvantaged in competition with other networks. If you limit the use or the reach of a social network, other networks who have more use and reach will grow faster. The reason the current major social networks are full of noise and over-engagement is not because people necessarily like that more or that other alternatives hasn't existed. It's because they won in the inevitable darwinistic battle a social network will join, where maximum reach and volume of content are key advantages.