who said there was? it's only on the scBTC which is why they will moved to the ZC SC in the first place; to get anonymity.
Here is exmple how to implement
ZC feature over BITCOIN block-chain
scBTC will not move to ZC.
1. We will create new SC over btc-blockchain
2. This new mixerSC can be mined by HMM and (Timestamp server or hashing Oracle)
Now you can use 2x swaps. BTC to mixerBTC and mixerBTC to BTC and you will have BTC mixed with 2 people.
Or you can use 2x 2wp. BTC to mixerBTC and mixerBTC to BTC and you will have BTC mixed with other 2 x N people.
Or you can deposit 10 BTC and withdraw 10 x 1 BTC.
You can do few random transaction in mixerSC to mix them more using mixerZC protocol (it will use same alg. as ZC, but that is all. No other connection to ZC alt-chain).
this reminds me of another point i wanted to make, unrelated to your post.
i find it striking that you and brg444, SC's strongest proponents on this thread, are so far apart on your vision of the #SC's that will arise. brg444 narrowmindedly tries to pidgeon hole the #SC's down to a mere two in his future vision; anonymity and faster tx times. you, otoh, openly say there will be billions. from your posts i can see you at least have imagination and an expansive mind, which is refreshing in and of itself unlike brg444, and i happen to agree with you when it comes to your estimate.
so i ask, if there are billions of SC's in action processing tx fees, where will all the badly needed tx fees come to support Bitcoin in the long run when the blockchain rewards are gone?