I speculate that you can't have anon on the blockchain. It is not secure enough to stand the test of time with your identity possibly being compromised because it is stored on a public ledger.
Your identity is not stored. What is stored are the transactions that move coins around, and the relationships between those transactions. Could that possibly be compromised in the future? Sure, anything could possibly be compromised.
In opposition to that premise we have:
1. That the cryptographic primitives used are mature, well understood and carefully scrutinized, making such breaks far less likely than newer techniques.
2. That the techniques used are defined in a formal mathematical way which make it tractable to fully analyze and prove their properties. This does not apply to methods that rely on complex implementations with no precise mathematical description.
3. That there are two separate methods being used, stealth addressing for unlinkability and ring signatures for untraceability. To fully compromise the chain to the level of Bitcoin's susceptibility to blockchain analysis you would need to break both. If one or the other were compromised, it could be replaced and coins moved so at least the privacy of current holdings would still be retained even if the other were later broken.
4. Nothing prevents using off chain mixing techniques in addition to the on-chain. Even ad-hoc ones like moving coins between a few busy sites like exchanges, gambling sites, in-person cash transactions, etc. This adds another layer on top of the base layer. But coins that lack such a base layer can never add one, they can only rely on the other methods.
5. If all of these methods were fully compromised then you have a situation that at its worst is no worse than Bitcoin. In all reasonable probability it is likely to be better.
AM is much more tech savvy than myself.
He later revised his opinion and stated that some form of on-chain anonymity is essential because it is the only way to preserve the end-to-end property (provable correctness without relying on the complex behavior of intermediaries). Check his later posts. He uses TPTB_need_war now.