I'm not sure how that holds. As much as there is value in privacy/anonymity there also is a lot in transparency.
I find myself mostly in agreement with your view that a private ledger could complement a public one but I'm not convinced this is sustainable if we somehow become able to transact privately within the public ledger.
That's the thing though; you can never transact privately when you start with a public asset. You can obfuscate the origin, kind of like proxies do now with internet traffic, but you can never have a true private asset. Bitcoin has what.... a headstart of a million users? That's nothing. There are still 6.998 billion people on Earth who don't use cryptocurrency.
I do see a future with a public and private ledger (perhaps even a good programmable ledger), but I am not sure which one will be more valuable. Ask yourself... if you were a powerful company or government, how much would it be worth to you to keep trade/state secrets?