Blockchain()com is a non-custodial online wallet; you should search for "custodial wallets" instead.
Interest-paying version requires KYC, you also need to send the funds to your main wallet if you want to send them out so you won't be able to "mix" your coins for obvious reasons.

I can't recommend you any custodial service since most of them have the same policy with Coinbase so you'll like get the same results when you use them for gambling.
Consider using a desktop client like Electrum and use the common privacy measures like never re-use addresses,
you can also send the funds to a couple of different unused addresses before depositing it to Coinbase; or just use a real mixing service.