I personally think the "God wouldn't do that" argument is a very poor one, no matter the subject.
.
It's a favorite among the conservative Novus Ordo types who simply appeal to Providence in attempting to make their case. "God wouldn't let that happen."
.
It's of course true, at bottom, that every proposition's truth is ultimately conditioned on Providence. But we have certain knowledge that provides a glimpse into God's pattern of design in a general way AND fairly accurate way. The testimony of the Fathers, the Universal teaching of the Church, etc.
.
When you just jump to "God would/wouldn't do that" you're *passing over* all the reasons that support or detract from arguing what God would or wouldn't do. It's basically question-begging.
.