Sure there's a lot stored, which does bring privacy concerns that are quite different from our current financial system, I'm not debating that, but it's not as obvious as you put it, as far as I understood it.
It really isn't that nuanced at all for Bitcoin. If I know your wallet I can see all of your transactions. Period. And if you want to trade money with me, you need to give me your wallet. Once I find it, thought, it is game over. [2]
There are "tumblers" that attempt to obfuscate the chain by turning one transaction into millions of little ones, but it is just a matter of tree search to reconstruct.
[1] https://www.rt.com/usa/158460-cia-director-metadata-kill-peo...
For blockchains in particular I think we tend underestimate the amount of information which someone with that kind of analytic capacity could derive, especially if they also have other data sources — for example, I would be quite surprised if the various anonymity schemes are less effective when evaluated as part of a full system against someone who has a lot of visibility into web activity (Google Analytics, Facebook beacons), DNS, email, etc.
If there's one thing I love most about the technology behind bitcoin, it is the permanent, public, unalterable ledger of every purchase I've ever made and every purchase I'll every make, and who I gave the money to. I'm super excited about the complete lack of personal financial privacy that Bitcoin's blockchain enables! /s