It doesn't solve anonymity, but it does solve the permission problem. You can transfer unlimited amounts of Bitcoin at any time and place without anyone's permission or approval.

But they can still come and beat you for it.

Other cryptocurrencies like ZCash, Monero, etc solve this in a more elegant way by making transaction actually anonymous.

While Bitcoin is not completely anonymous, it is also not completely transparent. The blockchain does not contain names and things can be obfuscated in various ways. Furthermore, a truly 100% anonymous system of money without any exceptions may not actually be desirable from a societal point of view, as it would enable things like assassination markets.

I'll also add that if Bitcoin had started out completely anonymous like Zcash, it likely would have been outlawed in many countries by now including the US and China. Certainly no exchanges connected to the traditional banking system would be allowed to exist.

Cash isn't really anonymous either. Serial numbers make it traceable, albeit with large time granularity. All banks and many large retailers track deposits and payments by serial number. That plus CCTV and cell tower data will usually be enough to identify someone with a pattern of spending dirty money.

But cash can move around quite a bit in a day. Spend $14 at merchant A, get $6 in change, spend $3 at merchant B, who hands that out to customer C as part of their change, who gives it to a bum, who in turn uses it to buy lunch... seeing a deposit of a suspect serial number at a merchant doesn't mean a whole lot. At best it gives you one more place to look through their CCTV and not find the guy you're looking for.