Reminds me of that priest who discovered he was baptized with the incorrect formula, and thus his baptism actually never happened. So they had to baptize him, give him all the sacraments up to Holy Orders, and then go and give all the sacraments to the people he baptized, married, etc.
They shouldn't have to redo marriages. The priest is the officiant but not the minister of the sacrament. The couple themselves administer it, having a priest present at all is merely a current discipline of the church to prevent abuse.
The priest only presides, yes. You redo marriages because the ministers were not following the correct form or were in the wrong state, or simply to issue a certificate when it had been lost in a fire, or something.
I think they tried to validly give the sacraments and all as much as possible, but at some point they couldn't get everyone, and so you trust it to God's mercy. He is not bound by the sacraments, after all.