If A seeks to assert ecclesiastical authority over B, but lacks power (be it physically or by persuasion and fear of damnation) to force B's submission,
Your presupposition of "ecclesiastical authority" is false, it violates religious freedom. ecclesiastical authority cannot impose truths. Truths can only be proposed to those who are disposed to receive it. There is no forced submission. Despite the actions of a few power hungry kings, forced conversions have never been recognized as valid by the Church. You sound like Brakelite.
then it is B's choice whether to submit to A's authority.
Yes, but on the grounds of reason.
I am convinced that the Catholic Church conforms much more closely to all of the
biblical data, offers the only coherent view of the
history of Christianity (i.e., Christian, apostolic Tradition), and possesses the most profound and sublime Christian
morality,
spirituality,
social ethic, and
philosophy.
I am a Catholic because I sincerely believe, by virtue of much cumulative evidence, that Catholicism is
true, and that the Catholic Church is the visible Church divinely established by our Lord Jesus, against which the gates of hell cannot and will not prevail (Mt 16:18), thereby possessing an authority to which I feel bound in Christian duty to submit.
If A doesn't seek to assert such authority over B, then A's power to force submission is irrelevant and it is always B's choice whether to acknowledge A's authority.
Agreed, but again, forced submission exists only in the minds of radical quasi-Christian cults that popped up <200 years ago.
The RCC no longer seeks to assert authority over non-Catholics, despite occasional pontifications.
The CC has never forced starving non-Catholics to eat food.
"occasional pontifications" are a light unto the nations to preserve the integrity of the family and the social order. For example, the death penalty is outdated and inhumane, given advances in rehabilitation, but the Church has no power over judicial systems. Same with abortion, a serious crime against God and man, yet we have formerly "Catholic" countries like Italy, Ireland, and Argentina passing liberal abortion laws. Where is all this "power and authority" the Pope is supposed to have???
"The RCC no longer seeks to assert authority over non-Catholics" presupposes the CC once sought to assert authority over non-Catholics. It doesn't work that way.