What will happen if eth adds anonymity to its blockchain? If it will be any need in XMR or zcash?
You can't add privacy like a feature, it has to be the raison d'être. As we saw from Zcash's experiment with opt in privacy, you end up with a small anonymity set and broken privacy.
They want to add z-snark to eth. And another problem anonymity on low volume coins is not very good, all these transactions can be traced easily. Only eth and BTC have great volume, so IMHO they can succeed.
The assumption that enough people will use it any given moment to prevent timing attacks is chimerical IMO--never mind that taint will happen regardless. Though this does highlight why Monero has no valid competition--it's not like it's hard if you have the resources to develop a privacy coin, but somehow everybody keeps repeating the same dumb mistakes. I don't know if it's greed (wanting to be both a clear and opaque ledger) or ignorance/arogance (not listening to the privacy minded community), but it's laughable how easy the competition makes it for Monero.