Lets say someone has a wallet, he receives coins from someone and sends some of them to another address. This happens more than once and at one point the coins from these change addresses are sent out too. Now you can pretty easily connect all the dots and you know with a high certainty that all the addresses that sent to those changeaddresses, belong to this one wallet. You might find out that this user has an investment in this or that security. And so on. Because the one who sent you coins first knows one of your addresses. If he can identify one of the sending addresses belongs to an exchange (there are tools for it out there) then he knows your other address is a change address. Since nothing other normally wipes out all the coins on the sending address. And when the coins from this change address are sent with other change addresses then he can identify even more of your wallets addresses. Not only the other change addresses.
The normal change addresses are a tool to connect addresses in one wallet. Thats why i dont use them because i dont know anymore where the coins came from. Where the are connected to. When i send coins to a FRESH deposit address on an exchange and receive the coins back to a fresh address on my wallet only then can i say that this address is secure. Of course you need an exchange with fresh deposit addresses. There are services out there that only provide one address for lifetime. Its way to easy then to connect all the addresses.
I do see that you have a point, which is stronger when addresses are reused. But I also think that you're overestimating how easy it is to know which address in a transaction is the change address and which is the other recipient(s), and overestimating the amount you should trust the third-party exchange to protect your privacy (sure, the blockchain no longer shows that your addresses are
maybe connected, but now Bitfinex and anyone able to hack or subpoena them knows your addresses are
definitely connected).
Third party exchanges are always a risk. Though i know of that risk and can act accordingly. I could chose another exchange or website that lets me do the same if i would be concerned.
You say its hard to say which address is the change address. I think its easy as long as more than one change address is used in an outgoing transaction. The thing is that transactions with more than one recipient practically dont exist. They are used by big websites mostly only. That leaves you with direct transactions and transactions with two outputs. And you can say with a very high certainty that those transactions are one involving a change address. Then you can use a website to automatically investigate. You might find out that one address belongs to an exchange. And yes, this is found out by the transaction connections happening inside the exchange too. So you identified the second address owned by that owner. And so on. When this change address is used as a source together with other (change) addresses then you know even more addresses that this wallet contains.
Ok, not reusing addresses can lower that risk to a degree. But the risk is still there because you dont have an overview about the change addresses and where they are connected to.
And there are enough services out there that pay out to the same address again and again. You cant change it all the time. Not to mention those users that use the same address for all of their transactions because they want to.
Unfortunately i dont find the link anymore. It was a tool where you could enter a bitcoin address and it could tell you with high certainty that it belongs to a certain exchange. Not so hard when all addresses are connected somehow.
I really wonder what happens if this get used to its fullest. I mean Bitcoin should become a big thing in the world. Nobody thinks about that it might be possible to identify the owner of some big stash. I think bitcoin is out of the game level and those are real risks in my opinion. Im not at risk unfortunately, or should i say luckily, because i took my really nice share of wrong going bitcoin investments. But i think about what comes in the future. Its not possible to handle things so careless if bitcoin will get real big.