There are many reason to have an anonymous blockchain. Think Wikileaks, ....., Whistle blowers, Investigative Journalism etc...
Yes - I can see the benefit there.
Fungibility. Good money needs to be fungible or the whole system of that money is inefficient as a medium of exchange and will inevitably break down.
It is not about anonymity per se but traceability. In the realm of digital money it must be untraceable to be fungible. Any piece of bitcoin must be indistinguishable from any other piece of bitcoin.
Anonymity can be a natural side-effect of untraceable digital money but is not necessarily a goal in itself.
The idea being that if I (Practical Dreamer) deposit 2 BTC to Wikileaks, and its
traceable back to me - then those 2 BTC then become worth a different amount (less) on the open market than they would if they had been 2 BTC transferred from the Queen of England to Barack Obama ??
How does that work ?
I can understand the idea of it being desirable for the BTC transaction to be untraceable (for our idealist purposes lets say a donation to Wikileaks) - but why would it make those 2 BTC any less fungible in the event of that transaction being transparent/traceable/not anonymous ? Why would they be worth any more or less ?
In other words, wouldn't BTC still be fungible without anonymity ?