Bellarminists can't address the problem of when heresy has become sufficiently manifest in order for deposition to happen.
1) Joe Sixpack reads a papal encyclical and determines that it's heretical.
2) Several priests and a bishop decide that the pope is a heretic.
3) Several bishops determine that a pope is a heretic but most other bishops disagree with them.
4) 49% of the Church's bishops consider the pope a heretic, but 51% don't.
5) 51% of the Church's bishops consider the pope a heretic, but 49% don't.
6) 90% of the Church's bishops consider the pope a heretic, but 10% don't.
7) General Council declares the pope a heretic and to have lost office.
Right now we're somewhere between #1 and #3.
Ok, everyone, let's put aside theory and talk about
real life. How/when does the pope get deposed? The above questions from Ladislaus must be raised again. I'll also step it up a notch. Riddle me this, and tell me what happens in this scenario.
Imagine you're living in a normal, sane catholic world, sometime between 1100-1500. A catholic cardinal, (not yet saintly but far from immoral, and who cares about the church) is elected pope, but the election was full of politics and manuevering because 2 powerful, italian families wanted their sons to be pope (actually happened a few times during the middle ages). The worldliness and ambition of many of the cardinals is boarderline sinful, with not a few living very scandalous lives. The major european kings of the time, who basically rule the world, while not openly at war, are constantly involved in little battles and skirmishes here and there, at various country borders, not amounting to the loss of many soldier's lives, but surely preventing the catholic world being at peace. Such small battles and constant bickering of the monarchs proved that while catholicism reigned as the religion of the world, far, far too many in the royal courts lived their religion with any kind of effort; most were immoral (including the kings). Let's also throw in some religious bickering, because, when has the catholic world not argued about something? So there was a large debate in the world at the time over the evils of nepotism and "alms" (i.e. bribery) given to bishops and cardinals, in exchange for help with political issues.
Into this make-believe world (which, if you read history, is not all that make-believe) a new pope is elected into the middle of political mayhem - with conflicts building in all 3 major areas of life - political, social and religious. The new pope has also said he wants to get rid of nepotism and the political corruption in rome. So 15 Italian Cardinals (out of 70) hatch a plan to get rid of this new pope, because they are friends of one of the uber-wealthy italian families. They are also supportive of the Italian-Spanish king, who is in 'disagreements' with France. The current pope's family is french, so of course, he is a political enemy of these 15 cardinals (even though the current pope cares nothing for politics and only for the faith and has openly said so. Again, he is a good man.).
Many of these 15 cardinals are very evil and caught up in the sins of nepotism and receiving alms/bribes. They talk to 10 other Cardinals who are politically neutral but who are also only Cardinals because of nepotism and bribery. So these 30 cardinals dream up a plan to claim that the new pope supports heresy. They plant false evidence, they get a few advisors of the Italian-spanish king involved in order to gain political support, as well as some of the governors of the italian provinces. The plan is set, the false evidence is brought forth and the wheels of conspiracy and lies begin to move. The entire college of cardinals is in shock, as is most of Italy. Of course, the rich italian family which stands to gain from the ousting of the pope is using every means possible to sway public opinion and tempt those cardinals who are neutral that 'everyone saw this coming' and that 'this pope has a lot of skeletons in his closet'. The 25 cardinals who are in on the plot are doing their best to contact every bishop and papal emissary who will listen and tell them of the pope's heretical ideas. In the end, based on public opinion, the pope is deposed. There is no trial, no council called to discuss facts, but the cardinals sign a letter which states the pope is to be removed, but this all happens 'after the fact' - with the letter being signed without discussion, just passed around like a birthday card for each cardinal to sign as a matter of formality - a testament to mob rule and the democratic extremes which are allowed (and encouraged) by Church law, for heresy in any degree must be removed at all cost, for the heretical man deposes himself. And the evidence against the pope was too damning. What other choice did the Cardinals have, but to kick out a deposed pope? The whole catholic world was witness to his heresy and self-judgement - there was no other option.
And so, with a +Bellarmine mindset, we must use this scenario to show the errors and extremes which a lack of due process and canon law procedures would allow, if the law was just simply 'a heretic deposes himself'. Such anti-heretical idealism is very catholic and sounds wonderful, but without practical measures and checks/balances, will lead to more mayhem and confusion than the actual heresy.