I agree that the Jews did that, but Nostrae Aetate waters that down.
Yes Jesus did intend for his religion to triumph. It is the only true religion and thus the great commission was to “conquer” the false demonic religions of this world. Most of that should be and was done peaceably, but the Church had a hard time with that with its people being killed keft and right. Of course martyrdom was used by God for greater purpose but He intended that the Church would grow and become mighty. What the symphony of Church and State did was allow Christendom to practice true religion under the protection of a king or emperor that would help protect true faith by beating back violent infidels (Charles Martel at the battle of Tourres kicking out the muslims, the Crusader States allowing local Christians to shirk their dhimmitude and practice the faith unmolested. etc) and also executing unrepentant heretics that were leading the faithful astray and found guilty in ecclesiastical courts. Heresy, scandal, and similar grievous errors are a form of spiritual homicide and to not repent from such is horrific and dangerous. Jesus wants as many souls saved as possible, but if there are false prophets leading the faithful away, a strategic put down of their leadership will save those many other souls, and the state has the right to arbitrate such justice.
Yes the HRE went through times of corruption as all states do. Jesus never said “Abolish the HRE, stop having kings and knights, and stop having my vicar anoint royalty and hold temporal power” he called for reform and repair. It’s time to shed the elementary school liberal civics and return to a true Christian social order. Perhaps something like Austria’s Christian Social party?
As for Papal Armies, the Pope did have military orders at his disposal in ages past and still dos today (albeit mostly ceremonial). I’m ambivalent about him having such, but you’re really reaching if you think I desire a “warrior pope” when the ministry of the clerical state precludes the shedding of blood. It is not befitting of a Pope to be a physical warrior.