You ask: what the hell is it about the Catholic Church as an institution that breeds such misery?

The problem is not limited to the Catholic Church, nor even to churches. It is entirely general: wherever a group of humans has power over another, there will be abuse.

This does not mean that all, or even most individuals with power will be abusers. It does absolutely guarantee that some will in all circumstances.

This generalises to other power structures in schools - prefects over other students, older or larger over younger or smaller - & in all other institutions. How many times have we read about similar abuses in military academies or 'in the field' between combatants or over prisoners or civilians? Within prisons, by officers over prisoners, or between prisoners? Among crews isolated on ships? Within gangs, clubs, teams... even within families (domestic violence).

This raises obvious moral questions: can groups safely be given power over others?

No, but equally obviously, they will be. Power heirarchies absolutely characterise 'civilisation'. A practical answer must be that whenever power is assigned to a group, oversight with power to intervene & an inescapable obligation to report (to the population at large) is also established. Even then, abuse will occur but at least will be detected, limited & compensated in a timely manner.

We do not say that power corrupts for no reason.