"Universal acceptance" is a modernist term coined by certain recent theologians that is often misused, in this case it is misused in regards to the status of popes.
First off, within the Church, whenever the word "Universal" is used, it does not mean a "current unanimity" at all, it only means the "current unanimity" within the Novus Ordo religion whose church was born about 1965.
Within the true Church, whenever the word "Universal" is used, it is inclusive of the element of time, as in, "since the time of the Apostles and for always", as well as possessing an "almost unanimous" consent of the Fathers, theologians and Catholic teachings since the time of the Apostles. So there is your first clue that "The Whole Universal Acceptance Issue" is NO.
So when one speaks of some "universal acceptance" as an infallible sign that the pope is the pope, we understand that whole idea to be an idea inspired and promoted by Novus Ordo thinking. OTOH, if it were in fact a doctrine or a teaching of the Church, which it isn't, but if it were, then it we are certain that like all future elections, the election will always have been deemed valid by the Universal Church, i.e. the Church of the previous 2000 years.
The false NO teaching (which many accept as if it were a true doctrine) referred to as "true popes" being "infallible safe" or the pope having some "infallibly safety", is also accepted by nearly everyone. Which "doctrine" basically means the pope is divinely protected from ever saying or doing anything that could do great damage to the Church. Little damages here and there he can do, but not major damage - that is basically their thinking as relates to the NO doctrine of "infallibly safety".
Meanwhile, since before the time of Pope St. Pius X, popes have written into the law of papal elections that the man, once he accepts his election, is not only "instantly the true pope", but also that "he acquires and can exercise full and absolute jurisdiction over the whole world". If this does not meet the criteria of popes' infallible safety, then nothing does.
So using the NO "doctrine" of "infallibly safety", what need is there of the NO "doctrine" of "universal acceptance"? Does not the idea of "universal acceptance" undermine, negate or otherwise demonstrate a decided and pronounced lack of faith in the idea of "infallible safety", rendering it altogether meaningless?