Well, they only need to cooperate in this sense to have the blockchain analysis entity feed them data about which UTXO's to block. But as I said, if they cooperate like this then it won't be long before that cooperation becomes a two way street, with them feeding data back to the blockchain analysis entity.
nopara73 has just admitted they would hire a blockchain surveillance company to analyze every single UTXO that join to participate in a CoinJoin transactions.
https://t.me/WasabiWallet/63992