Agreed on most of the points. True, church provided some legitimacy not all of it and not even majority, secular rulers had a lot of power over local clergy due to many factors and by the 10th century rulers tried to usurp church completely (e.g. emperor named new pope after old one dies). Bishops literally sworn fealty to HR emperor, and in some places monarch chose or at least had ability to choose who will become abbot or bishop or whatever.
Agreed on most of the points. True, church provided some legitimacy not all of it and not even majority, secular rulers had a lot of power over local clergy due to many factors and by the 10th century rulers tried to usurp church completely (e.g. emperor named new pope after old one dies). Bishops literally sworn fealty to HR emperor, and in some places monarch chose or at least had ability to choose who will become abbot or bishop or whatever.