deanonymization could be easier
I didn't think mainly about deanonymization, rather I thought about confirming more transactions per block without increasing the maximum block size. It could be especially useful when we have something like this in mempool:
A -> B -> C -> D -> E -> F -> G
Then, the miner could create a "CoinJoin proposal" like this:
A -> G
And if A will sign it, the miner will save some space. If not, the miner could propose something else, for example:
A -> B -> G
Of course, when we have N transactions in mempool, there are 2^N-(N+1) possible combinations of such "CoinJoin proposals". To avoid spam, we can add some nonce and difficulty to them (since such proposals are "not-yet-signed-by-all-participants" transactions). And if the miner won't collect all needed signatures, it can still use the original non-CoinJoin transactions.