But the problem is overgeneralization.
There are countries whom are shallow Muslim countries. Countries that prioritize national values over Muslim values. Further, the overgeneralization may cost punishing decent people on the individual level. My point is that when this is done it may increase terrorist recruitment.
Your position is that being cautious in dividing the wolves from the normal people may too be perceived as a weakness. That the normal people may turn wolves and use this weakness to attack and hide behind an "ordinary civilian" camo (if you will).
So to summarize, it seems the problem is between overgeneralization and identification. We do not want punishing normal people and we cannot differentiate and identify the culprit between them at the moment. Not until they perform their terrorist acts at least.
Kinda makes you wish you had a mind reading device, does it not?