I don't know about input amounts since blockchain is anyway transparent and accessible to everyone, but it definitely makes sense to not share with a coordinator the information that is not visible on the blockchain. For example, you have two outputs in your wallet, one of which came from your verified account on Binance, and the other came from a mixing service such as Chipmixer. These outputs have no connection with each other, except that their private keys were derived from the same seed words. When you register these outputs for a CoinJoin transaction, a coordinator may learn the fact that these outputs are linked to each other, and also he will know that some of Binance customers used a mixing service. A coordinator keeps records of all inputs and hands over this information to a blockchain surveillance firm or law enforcing agencies directly. Another example is when you're merging your coinjoined output with non-coinjoined output or with toxic change. In this case, it also becomes trivial to deanonymize you because by merging with unmixed outputs you make the whole process of mixing worthless.