I'm not saying that Joffrey was a "good" leader. It's obvious that he was a horrible leader. But, he would have protected his family from every outside threat. If anyone was going to torment his family, it was going to be him.
Tommen doesn't have a clue as to what he should do. He's weak and timid, and those are the wrong characteristics for a king. As soon as the High Sparrow took his Mom, he should burn the building to the ground, and killed everyone in it. By them taking his Mom, they showed him that they have no respect for him or the crown he wears. No one should ever even dream about taking your Queen, and you're a sitting King. That's why some countries use regents when the king/queens are young. They have too much chaos going on in the kingdom; they just can't afford a timid king right now. If he can't deal with the High Sparrow, he for damn sure can't deal with White Walkers or Dragons.
On top of all that, he has horrible advisors. Westeros is doomed if he stays king. He needs Tyrion more that anyone.