There obviously were conflicts between the papacy and the emperor of the HRE. The emperor would appoint an antipope to replace the pope. The title of pope also came with land and had secular power besides being the spiritual leader of the Catholic church. So why didn't any emperor try to become pope as well?
-There were often conflicts between the Holy Roman Emperor ( HRE) and the Pope over which one of them held ultimate spiritual authority. As the Holy Roman Empire gained power , the HRE began to be considered a great religious leader, not merely a secular leader. So the conflict was not so much about who had the most power in general as it was about who had the most power in the church. The HREs did not want to BECOME Pope, they wanted to subvert the Pope’s authority and become supreme religious leader in his place.
One very important thing would most likely be lost if a HRE were to become Pope- the chance of an heir. The Pope was, with some exceptions most of which occurred during the Renaissance, chosen from among higher- ranking churchmen. Clerics were required to be celibate, and therefore would have no heir. There were cases of Popes having sons who also went on to be popes, most notably the Borgias in 15th and 16th century Florence, but again these were exceptions rather than the rule. The HRE, because he was designated ruler of an Empire, needed the security of an heir to keep the power in his line and keep the empire running after his death. Thus having to go through the process of becoming part of the Church would be suboptimal for an HRE attempting to secure his secular and religious authority.
The HREs were actually crowned by the Pope . Anyone could become the ruler of the area consisting of Germany Burgundy and Italy without any church approval, but to actually be the HRE the Emperor had to go through a process of gaining the Pope’s approval and being granted the title. So the entire delicate and complex system would have fallen apart if a HRE had tried to become Pope.
Edit: formatting and a typo