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.