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because gossip announcement channel size can be easily correlated with coinjoin input.
Public channels reveal to the world exactly which UTXO was associated with the channel; private channels do not. This is why mempool.space can label public LN channel opens with node IDs. For example: https://mempool.space/tx/37b07c1917fe814c4b504bd5a6746dd05d8140d6012d7d8b0e4321d91620db8d
LN does this as an anti-DoS measure. Without something similar to this you'd be able to advertise an infinite number of channels to the gossip network.
Exactly that. Private channels already hide finding UTXO, and the public ones cannot even with coinjoin. Unless all inputs will be equal.
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