Joseph Gill summarizes the trouble with the later phases of the Council of Basel:
…The Conciliarists, particularly those of Basel who carried the theory to its utmost limits in order to affirm that a council is by Christ’s ordinance the supreme authority in the Church, were constrained to deny that St. Peter was ever head of the Church. That was a conclusion new to the West, born of the crisis of the Great Schism. The [Basel] Conciliarists wanted to make it permanent and to provide it with the machinery of action. If their ideas had prevailed, the world would have seen the spectacle of general councils summoned every ten years and being to all intents and purposes in permanent session, not only guiding the faithful in what to believe but directing the day-to-day business of curial offices. As a theory it was a novelty that would have turned the constitution of the Church upside down. As a system, it would not have lasted long, for it would soon have been torn to bits by national rivalries and personal intrigues. What would have followed, who knows?:”(Eugenius IV: Pope of Christian Union [Westminster, MD: The Newman Press, 1961], pg. 211.)”:
It should be noted that the radicalism Gill describes was not held by the conciliarists at the Council of Constance (e.g., Pierre D’Ailly and Jean Gerson), nor by one of the most eminent of men who participated in the early phases of the Council of Basel, Nicholas of Cusa. What Gill is describing is truly radical conciliarism, and against this the papalist reaction both then and today makes perfect sense. When set against the more moderate conciliarism of D’Ailly, Gerson, and Cusa, however, it is the papalist reaction which begins to appear radical.