I'm not grasping your idea yet. Does it hide any information from the public network? What is the advantage?
If at least 50% of nodes validated transactions enough that old transactions can be discarded, then everyone saw everything and could keep a record of it.
Can public nodes see the values of transactions? Can they see which previous transaction the value came from? If they can, then they know everything. If they can't, then they couldn't verify that the value came from a valid source, so you couldn't take their generated chain as verification of it.
Does it hide the bitcoin addresses? Is that it? OK, maybe now I see, if that's it.
Crypto may offer a way to do "key blinding". I did some research and it was obscure, but there may be something there. "group signatures" may be related.
There's something here in the general area:
What we need is a way to generate additional blinded variations of a public key. The blinded variations would have the same properties as the root public key, such that the private key could generate a signature for any one of them. Others could not tell if a blinded key is related to the root key, or other blinded keys from the same root key. These are the properties of blinding. Blinding, in a nutshell, is x = (x * large_random_int) mod m.
When paying to a bitcoin address, you would generate a new blinded key for each use.
Then you need to be able to sign a signature such that you can't tell that two signatures came from the same private key. I'm not sure if always signing a different blinded public key would already give you this property. If not, I think that's where group signatures comes in. With group signatures, it is possible for something to be signed but not know who signed it.
As an example, say some unpopular military attack has to be ordered, but nobody wants to go down in history as the one who ordered it. If 10 leaders have private keys, one of them could sign the order and you wouldn't know who did it.