Cross-chain analysis trivially links transactions in which people swap Bitcoin → [X] → Bitcoin; and due to subset sum analysis and timing correlations, it is surprisingly difficult to avoid all practical potential of linkage or probabilistic linkage.
Isn't that much more difficult to do for the average, non-government, or non-ciphertrace / chainalysis group? Of course it can not be "proven" if there is indeed a link since they are cross chain.
What if there is a certain amount of time that passes by between the swaps, or if the swaps goes through different exchanges? You mention PayJoin and CoinSwap, are those different from CoinJoin and the other things Wasabi (the wallet) are trying to do, or doing?