> My understanding is that forbidding priests to marry stems from a desire to maintain the wealth of the church
As I understand it, the discipline in the Latin Rite of the Catholic Church forbidding priests to marry was a response to a epidemic of scandal in the medieval church of priests neglecting or misadministering their clerical duties for courtship and family issues. Church property isn't personal property and can't be inherited even if you have children.
My extremely limited understanding matches what you say as to the history, but in support of the previous comment while a priest's family cannot inherit from the church, the church can inherit from the priest.
As I understand it, the discipline in the Latin Rite of the Catholic Church forbidding priests to marry was a response to a epidemic of scandal in the medieval church of priests neglecting or misadministering their clerical duties for courtship and family issues. Church property isn't personal property and can't be inherited even if you have children.