Not doing business with mixers: wow, what an interesting way to stir up trouble! Someone should create a service to distinguish "legit" from "tainted" Bitcoin. Let's see if Gresham's law applies so 1 bitcoin is no longer 1 bitcoin. What would the other exchanges do if one of them started trading these separately?
It's important to distinguish two issues: (1) whether the currency is usable as currency and (2) whether there are forensic clues enabling law enforcement to identify criminals. They're completely separate questions.
The value of a dollar bill is the same whether it was used in a crime. But if it has some ink on it, it might provide evidence that the person holding it robbed a bank. The ink doesn't keep the dollar from being usable.
It has to be this way. Otherwise money simply gets taken out of circulation, and people participating in the economy have to worry about whether money is money.
More: https://www.reddit.com/r/Bitcoin/comments/1qomqt/what_a_land...
Say I steal 10 bitcoins from you. I go to someone who cleans bitcoins for a cost of 10%. I send them 10 bitcoins, and they send 1 bitcoin to 9 different wallets (keeping the 10th as payment). That alone would allow you to still track it. But now add in thousands of other people sending them bitcoins on the same day, and some random pauses as to when they send the bitcoins to other wallets, and you are no longer able to tell which bitcoins in are associated with which bitcoins out.
Now, do you just get businesses to stop doing business with anyone (any wallet) that has ever received bit coins from the mixer? And there are many mixers out there.
And this is still simplified. You can be governments are monitoring and running statistical analysis on those mixers to try to find people laundering bitcoins associated with especially bad things. I'd even guess some of the bitcoin laundering operations are ran by governments in an attempt to better track the flow of bitcoins.