Zcash won’t be the next coin added for the same reason Monero won’t. Coinbase is tracking their transactions a few steps and close accounts if you withdraw to some P2P exchanges or gambling sites, etc. It’s all in their terms of use and that’s simply not possible with Zcash. I think Coinbase will not add privacy coins.
Interesting @mrkwh, I'll go have a look at Coinbase terms of use, i'v also noticed they've just updated their privacy policy
The Update of Coinbases terms of use were due to new European laws, they now have to save trading datas of their customers for five years, and every exchange has to do an AML/KYC reasoned verification.
humm, that's bad news, you would think data privacy laws like the GDPR would lead Coinbase to collect less data, not more, I am surprised