Why doesn't the Pope try asserting doctrines ex cathedra to check if they're true? My understanding is that the Catholic Church teaches that when the Pope speaks ex cathedra, he is infallible, because what he says in such instances is divinely protected from error. There are a lot of questions that the Church considers open, e.g. the question of whether infants who die without being baptized are saved. It seems like it would be a great idea for the Pope to attempt to assert ex cathedra that they are saved. Either the pronouncement would succeed, in which case we would know with certainty that it is true, or else something would prevent the pronouncement from going through, in which case we would have a hint that it is false.

I assume that I am misunderstanding something about papal infallibility and there is a catch somewhere. What's the catch? Naturally, I'm interested in the teaching of the Catholic Church.

Here are a couple of possible answers:


Technically, the Pope could "exploit" infallibility in this way, but it would be immoral.
If the Pope decided to try this sort of thing, he would be divinely prevented from making the ex cathedra pronouncement regardless of whether the doctrine in question was true or false, so we wouldn't actually learn anything from the exercise.


In either case, I'm left wondering: What exactly differentiates "legitimate" ex cathedra pronouncements, like the pronouncement of the immaculate conception in Ineffabilis Deus, from the sort of "illegitimate" ex cathedra pronouncement that I suggested?
Pope Pius XII—in his apostolic constitution that defines the dogma of the Immaculate Conception, Munificentissimus Deus (1950)—describes the process in which he sought counsel from all the bishops of the world in the letter Deiparæ Virginis Mariæ (1946), where he asked them (§11):


  Do you, venerable brethren, in your outstanding wisdom and prudence, judge that the bodily Assumption of the Blessed Virgin can be proposed and defined as a dogma of faith? Do you, with your clergy and people, desire it?


The response was almost unanimous.

Although a pope has the authority to define a dogma without asking for counsel regarding its "definability," it would be rash not to seek counsel.