At least 870,000 bitcoins are associated with illegal activities. This is about $ 10 billion.
....
One day, all these bitcoins will somehow hit the market.

So what?
There is no doubt many more 10's of billions of dollars in fiat associated with illegal activities.
Fun Fact: At least in the West, check any large random sample of paper currency and there will be traces of cocaine on much of it. Does anyone worry about that? No.