Peters made two arguments: a tactical one (”a demand that has not been made”) and one on the merits (”very serious negative consequences for couples”). The matter of tactics indeed needs to be decided; possibly right now it is not a good time but perhaps at some future point that is, no doubt, coming nearer, it would be.
The argument on the merits is plain wrong. The Sacrament of Marriage confers grace on the married couple. That is not altered by the proposal. That the state also might have “tax liabilities, insurance coverage, property ownership and inheritance” altered by the marriage, the state originates them, not the Church. If the spouses see an advantage in being registered as married for those privileges and liabilities, they are free to go and sign the papers in the city hall.
ALL priests, pastors etc have been required to be notaries. The state (whichever) does not recognize the priest/pastor/etc. the state (whichever) recognizes the notary status.