I don't think they'll stop until governments become harsher on the refugees, especially before the start of winter.
And, yes, Europe's borders never should have been so open. It'll eventually cause even worse problems than it has thus far.
I don't think open or closed borders really matter. It's just the way European countries deal with the migrants in the end. If they closed the borders, we'll see footage of thousands stranded on Greek islands and the European "scum". They'll be painted as an enemy by Muslims for every right-wing stance they may take on the Muslim migrants. They'll be painted as a hero by Muslims for every left-wing stance they may take on Muslim migrants.
For example, when Angela Merkel decided to take in 500k migrants:
Why do we almost never see rich non-Western countries like Japan and South Korea taking in refugees?