Of course they're not going home by choice but this is not the point.
The sitution is changing drammatically in Syria and in Iran also. And 80% of the migrants stated they are from Syria, because that gave them a legit refugee status. So now Eastern Europe with Austria and Italy can (and I think will) change the narrative to let's ship them home. Because actually international EU law allowes to kick them out if their country is safe enough.
So it is not their choice to go. It will be our choice now.