I have given you ample examples of madrassahs teach terrorism techniques. Hundreds of other examples you can find by yourself. You are only deluding yourself here.
Many takifirs do come from secular institutions or such, but they are a smaller (but equally dangerous group), but many of them are influenced by madrassah educated mullahs. The impact of the madrassah cannot be overstated on shaping society's opinion even if not everyone attends a madrassah. After all madrassah graduates go and preach at masjids. Why are you trying to devalue the influence of the madrassah on pakistani society?
but clearly it can be and it is being. Terrorism isn't linked with madrassa or beard or being a hafiz. Although right now pakistan is mobilising its army to combat with those who hail from madrassas. However there are ample examples of those who fall in the other category and are ignored because we donot have any pressure from western countries to deal with them. Therefore the link between madrassas and terror is a mote one. Madrassas essentially is a place which teaches you Quran, hadith ,fiqh and shariat. Since our govt fail to provide opportunities in govt run institute to cater to religious education we see madrassas. It is extremely disingenious to conclude madrassas are a source of terror. As for the writ of govt being challenged that is being challenged every day in pakistan by most memebers of the establishment and quite flagrantly too. The reason there is a battle going in northern areas is because we are only cracking down on these ones.