I probably don't want my coins to still have someone else's history attached to them, in case my trading partner looks at them and (as an example) sees they've come from a wallet with 50 BTC in it and then decides I'm now a target to be robbed.
Your concern is quite justified: no one sane would want to attract the unnecessary attention of scammers and robbers by demonstrating wealth that is not even yours. Also, no one sane would want to attract the unnecessary attention of law enforcement agencies by swapping sweet clean coins with coins connected to illegal activities such as money laundering, terrorist financing, hacks, or the purchase of prohibited literature. If your counterparty checks your transaction history, you're in trouble: they will attempt to rob you in the former case and will hand you over to the police in the latter. Do you see the main problem? Despite any reasonable objections of privacy/freedom advocates, bitcoin is non-fungible because it has an in-built transparent history. How do we make bitcoin more fungible? We either need to make bitcoin completely non-transparent, which is impossible for many reasons, or we can make its transparency work for us. The broad use of such tools as Mercury wallet or coin swap may help to make blockchain's transparency a less reliable source of information for undesirable observers. If every transaction in the blockchain is broadly known to be the result of a swap, it will be harder for a potential observer to find out who owns what, and who makes transactions with whom. If a robber is not sure you really have those coins, he is unlikely to make you a target.