Oh, you're right about there is no obstacle, and when the idea of blowing up the bridge come up, it was cut by the idiot, and never addressed.
If later there's a stupid reason for letting that bridge up, the soldiers are not going to be happy to that.
Defending a bridge like Benkei, and The Berserker of Stamford Bridge is a romanticized story, young man. Search for your medals in school sport festival.