P.S. Rome does not kill, although Priests may.
Bishops, Cardinals and Popes in history have been responsible for killing personally as well as ordering slaughter. Collectively, what would you propose to call them, if not Rome? The Papacy? The Hierarchy? The Magisterium?
When a pope and council requires RC rulers to exterminate those she defines as heretics then it is indeed Rome doing the killing, if by proxy. Denial of that is simply sophistry.