Monero and Grin/Beam are also public ledgers. But they are harder to deanonymize. You brought a non-sequitur.
The CoinJoin paper details the level of anonymity that it can offer. I could cite it to you here, but I am not convinced that you would read it if I did.
The level of anonymity it can offer is zero. All you can do is obscure the recipient of an outgoing payment or the sender of an incoming payment. We still know all the cash flows in and out of every single address in the network.
