Not quite "holds the keys", more "honours the balances".

If I hold an account balance which I KNOW I can exchange for a higher order form of money (e.g. the bike in the example above or physical gold in the example of gold shares / gold backed currency) then I don't need to worry about redefining my account balance as money in its own right. A trusted 3rd party has already 'rubber stamped' it for me.

Cryptocurrency, however, has no such rubber stamping 3rd party other than the public. It therefore has a far bigger challenge to meet than supporting privacy and that is supporting value. (i.e. arriving at a public consensus that it is money, and base money at that).

As I've posited above, any obfuscation whatsoever of the base monetary media, just inhibits this evolution of a public consensus definition of base money. As an absolute base minimum you need to have all the following aspects exposed to the entire userbase of the system at all times for every address:

For any given address at random:

[1] - all the transactions that contribute to that balance (all inputs)
[2] - all the transactions that depleted that balance (spends)
[3] - the originating addresses for [1]
[4] - the destination addresses for [2]

That is a public audit for a given address balance that will support a public consensus of its integrity and veracity. No amount of math formulae or cryptographic b.s. substitutes for such transparency.

Although one person cannot go through every address in the blockchain to satisfy themselves of the global integrity of the system, the aggregation and general network effect of millions of people doing so every minute and every second of the day is an endorsement that no trusted third party, nor any cryptographically obscured blockchain could ever match.

People with "Fiat heads on" and a "Fiat mindset" see these balances as corresponding to people. They do not. They are anonymous as cash is. Just because you can see the originating address of a transaction doesn't tell you what the nature of the transaction was and whether money changed hands or just moved between two addresses controlled by the same person. It doesn't tell you if the controller was initiating a transaction on behalf of someone else, themselves or even if it was an automated transaction.

As for gleaning information from outside the blockchain, that is mitigated by maximising the fungibility of the monetary medium (which is, as I keep repeating, not the same as maximising its obscurity).

It is not the job of a monetary media to support the privacy of its holders beyond - in the case of cash - maximising fungibility (which IS one of the recognised monetary properties) . Its job is to efficiently store value and to that end a publicly defined currency needs a public blockchain that supports a public audit of the kind I just described.