The general plan was, and is still, to stop using v4 once it stops being useful, in much the same way that people stopped using IPX when it stopped being useful. (By which I mean: people still use IPX today, but in general you don't need to think about it.)
You can do private networks on v6; there's a massive range allocated for them (fc00::/7).
In general, v6 is designed just fine. Most of the complaints you see are from people that either don't know what v6 can do ("why didn't they just implement <thing that v6 already does>?") or don't realize that what they want is impossible ("why not just ignore the pigeonhole principle?").
You can do private networks on v6; there's a massive range allocated for them (fc00::/7).
In general, v6 is designed just fine. Most of the complaints you see are from people that either don't know what v6 can do ("why didn't they just implement <thing that v6 already does>?") or don't realize that what they want is impossible ("why not just ignore the pigeonhole principle?").