ehm, no. you can create brand new wallet for each transaction and wallet on its own is not connected to your real identity in any way. it's more like government's worst nightmare.

As I understand it, if you want to receive bitcoins with wallet A and send those same bitcoins with wallet B, you would need to transfer said bitcoins from wallet A to B. And each transfer is recorded in the blockchain.

This is correct. However, it is difficult to prove that A and B (or perhaps every wallet in some long chain) are owned by the same person, especially if everyone has a large number of wallets and doesn't reuse them when they are empty.

Let's say the blockcoin shows a transfer of 1 BTC to a new wallet A, and then to a new wallet B, and then from B to a wallet owned by a registered BTC-USD exchange C; to comply with government regulations and protect themselves against fraud, C checks the ID of the owner of the wallet B. A government can now determine the identity of B (and might even force C to provide the information on all transactions in real time, so they know who B is even without an investigation), but they cannot automatically infer the identity of A. There are two possibilities: Perhaps A is owned by a different person, who earned BitCoin for doing some work, and then purchased another service from B. Or perhaps A and B are owned by the same person.

In reality, this might not be the only piece of information available, and governments will probably want to use statistical techniques to estimate the probability that a particular address is owned by a particular person, combining all evidence. They will likely take into account all points where money comes into or leaves a wallet with known identity (e.g. in USD -> BTC transactions or BTC -> USD transactions), and the structure of the network between those transactions. For example, suppose wallet A, B, and C are known to be owned by the same person, and someone moves money from all those wallets into wallet D. Then governments will probably infer that D is owned, with high probability, by the same person as wallet D (because multiple low probability pieces of evidence can combine to give a higher probability). Of course, the transactions are not independent, because the owner of A, B, and C might just be a regular customer of D - timing evidence might be taken into account, along with other evidence about the identity of D (for example, does D only receive money from the owner of A, B, and C, or from other sources? Where does the money go after that)?

> but they cannot automatically infer the identity of A.

They can certainly walk up the tree though, which is impossible with cash but extraordinarily easy with BTC. In this case B could have a tax bill to pay unless they can prove otherwise.

It sounds like you're talking about extremely trivial money laundering; while it might have caused some confusion a century ago when the Mafia started doing it, modern tax authorities deal with a hell of a lot worse.

It's more traceable than cash, less than bank accounts.