Not entirely true, as that unspent output need never be touched. I can move my other coins which I had in this address to another which is now clean, without touching the dirty dust that you sent me.
If I send it to a cold wallet address of an exchange where another 7000 BTC are stored, is it still simple to sort it out?
Of course, if received to a fresh address it as manageable.
It makes no difference. Bitcoins at an address are not automatically mixed together. As aantonopoulis says, you can just ignore the attackers output. Some wallets include the feature "coin control" which makes this much easier to do.