Archipelago: a private network built on Ripple

[xourexe]

I didn't know about this private implementation of Ripple:

https://spar.ro/archipelago/

And I'm having a hard time imagining how these private networks fit together with the public network. By making an analogy with TCP/IP netwoks, I can imagine that the public network will connect private networks with each other as well as with other entities operating on the public network, but I can't see clearly the benefits and incentives for operating on the public network instead of doing it all the time on a closed network...