After all, a non-bishop (layman or mere cleric or even priest) cannot be the Bishop of Rome.
Yes, but he can be pope. A layman can be elected pope, he should just become Bishop of Rome immediately afterwards IF he accepts the papacy, according to Canon Law. According to the 1917 Canon Law, it is merely required that he is a priest before the election (before 1917, even laypeople could be pope, St. Fabian in 262, John XIX in 1024, etc.).
So, if I get elected as a priest, but say "I don't accept the papacy", I stay and am priest and nothing happens. AFTER I accept, it is necessary that I should be made bishop, if I'm not already, but it is not a requirement for the designation or election. There can indeed be a weird situation where someone is pope, but not Bishop of Rome (yet), see "In Nomine Domini" from 1059:
- If war or other circuмstances prevent a papal enthronement or coronation of the elected candidate, the candidate will still enjoy full Apostolic authority.[7]
https://en.wikipedia.org/wiki/In_nomine_Domini
The "material pope" theory is metaphysically impossible, since the goal of the papacy is papal jurisdiction, not being a material representative. And the goal of jurisdiction is absolutely inseparable from the matter of designation, as it precedes the papal election: The jurisdiction is the "perfection" of the designation, but without this perfection being possible (due to heresy as privately judged by laymen), any designation becomes pointless. If I accept "the papacy", I accept the jurisdiction of the papacy, not just the nice white clothes. And all post-VII popes, have, at least in their words, accepted the jurisdiction, for better or for worse.
This same principle applies to baptism of desire: The moment where I say "I want to be baptized", I accept the goal which is a Catholic baptism, in order to obtain the remission of sin. At that point I am not in limbo, so neither is a designated-accepted-but-not-yet-bishop pope. A pope saying "I accept the papacy" is not in limbo, he has the office of the papacy, period - even if he isn't consecrated Bishop of Rome yet.
He should however be consecrated bishop immediately afterwards (says Canon Law), because that is the proper form for the papacy. Otherwise, you couldn't even ask the question "do you accept the papacy" to a non-bishop (because he couldn't accept it), but Canon Law allows asking this question to a non-bishop. Similar to someone wanting to be baptized taking RCIA classes in order to get baptized later - if he dies in between, he is still baptized.
Without the goal of baptism being possible (let's say a hypothetical earth that contains no water, so a physical baptism being impossible), my desire for baptism would be pointless - so also without the goal of papal jurisdiction being possible due to material heresy, the entire act of papal election would be pointless. There cannot be any matter of papal election without the possibility of the next pope obtaining papal jurisdiction, it would be a nonsense election.
Bishop Guerard eloquently explained the distinction between matter/form distinction applied to the papacy is not of the absolute ontological variety.
Oh he did say that, sure. Problem is, he's wrong as the distinction is ALWAYS absolute. He leaves St. Thomas and basic reason completely behind. Nobody has ever seen a block of wood having matter but without form - similarly nobody has ever seen a pope having matter, but without form. That's because the word "wood" means "structural tissue of trees" and "pope" means "someone who has the jurisdiction of the papacy" - "pope" does not mean "someone who runs around in white clothes" or "someone who was nominated to potentially, in the future, accept the jurisdiction of the papacy".
And before you say that I cannot apply this principle to offices since they are not material goods - "king" for example does not mean "someone wearing a crown" as anyone can do that, it refers to the power of the king. So yes, I can apply the matter / form distinction 1:1 to offices, too.
If I get nominated "pope", but I don't accept, I have never, not for one second, been "pope", simple. The moment I accept however, I have papal - extraordinary - jurisdiction, even if I'm not immediately dressed in white clothes or . There is no limbo, especially not one that could be blocked by heresy. So, the word "pope" refers to the jurisdiction not the designation, similarly to how the word "baptism" refers to the act, not the water it is performed by.
Form precedes matter, matter does not precede form. If achieving the form is impossible due to heresy, then so is the matter. There's more information
here and
here.