Lightning network just does net settlement to the public chain, and very infrequently, so it’s somewhat more private.
> anyone is free to contribute and build on top of it
These are great features, certainly welcome. However, I believe my point still stands, bitcoin is not philosophically 'private' indeed the entire basis for it working is that it is a public ledger (yes more private crypto does exist, like monero, but the conversation is about bitcoin). The public ledger is the feature, not a bug.
One day it might be all those things, one day I might be pope. But you can no more say it is that than you can say I am his holiness.