I have noticed that EOS may support side chains, and that is one method of scaling transaction rates. It reminds me of sharding or Plasma in Ethereum. So, EOS will probably match their scaling capability there.
It also seems to me like it would be possible for EOS to implement something similar to off chain state channels like Ethereum's Raiden, so I'm not worried there.
However, it appears Vitalik is saying that the same zero knowledge proof techniques that can be used to bundle different transactions together for privacy can also be used to bundle them together for scaling purposes. In the linked post, he says 500 transactions per second is a reasonable expectation. Certainly EOS supports more, but the advantages are less clear if the fairly ubiquitous Etherum is no longer so low.
My read is that Ethereum is still the top currency for developers, even though EOS is making inroads. I also believe privacy is a powerful motivator for users and app providers. However, it doesn't seem like Dan Larmier is keen on implementing it on the merits of privacy alone.
It is difficult to convince everyone that the 21 block producers represent a good tradeoff for speed vs. decentralization currently. If Ethereum implements this speed/scaling solution unanswered, I fear users and developers will have much less reason to switch to EOS, so I'm wondering: Is it possible for EOS to implement ZK-SNARKS/ZK-STARKS, if not for the attraction of privacy, then simply to protect its main advantage in speed?
If we were just considering privacy by itself instead of speed, maybe an argument could be made for using address/account hopping or possibly tumbling, but I remain skeptical as to the ultimate effectiveness and safety of those methods given what has happened in the past with bitcoin.