Question

The Catholic Church supported the claims of the monarch

Answer 1

The ones offering the best bribes (or had control of the Pope) ended up with the franchise rights.

Religion was not created to enlighten, it was the first mutual admiration society. The high priest who controlled the biggest, most popular temple would anoint a local king with a monopoly on the right to rule the area. This would be done with magic wands and pomp and circumstance, and the masses, suitably awed and impressed, would fall in line. Then the king gave the high priest the religion franchise and they each watched the other’s back. This was basically how the hoodwink worked until the Romans merged state and religion, so their rulers often anointed themselves and served as high priest and emperor until Constantine severed that connection by handing over the Domus Laterani to the Bishop of Rome.