Well, it wasn’t as if people didn’t believe in Mary’s Assumption before 1950, or in her Immaculate Conception before that was formally declared dogma, in 1854. They were both very high level teachings that easily could have been considered dogmas (or dogmata, if you prefer) already. (There are books out there, like Ott’s book on dogma, which go into which teachings have what priority level, and what stuff is considered dogma.)
The apostolic constitution “Munificentissimus Deus,” which defined the dogma, points out that people had been petitioning the popes like crazy since the Immaculate Conception dogma was defined on Dec. 8, 1854:
"…the minds of the faithful were filled with a stronger hope that the day might soon come when the dogma of the Virgin Mary’s bodily Assumption into heaven would also be defined by the Church’s supreme teaching authority.
"Actually it was seen that not only individual Catholics, but also those who could speak for nations or ecclesiastical provinces, and even a considerable number of the Fathers of the Vatican Council, urgently petitioned the Apostolic See to this effect.
"During the course of time such postulations and petitions did not decrease but rather grew continually in number and in urgency. In this cause there were pious crusades of prayer. Many outstanding theologians eagerly and zealously carried out investigations on this subject either privately or in public ecclesiastical institutions and in other schools where the sacred disciplines are taught. Marian Congresses, both national and international in scope, have been held in many parts of the Catholic world. These studies and investigations have brought out into even clearer light the fact that the dogma of the Virgin Mary’s Assumption into heaven is contained in the deposit of Christian faith entrusted to the Church. They have resulted in many more petitions, begging and urging the Apostolic See that this truth be solemnly defined.
"In this pious striving, the faithful have been associated in a wonderful way with their own holy bishops, who have sent petitions of this kind, truly remarkable in number, to this See of the Blessed Peter. Consequently, when we were elevated to the throne of the supreme pontificate, petitions of this sort had already been addressed by the thousands from every part of the world and from every class of people, from our beloved sons the Cardinals of the Sacred College, from our venerable brethren, archbishops and bishops, from dioceses and from parishes.
"Consequently… we commanded that, by corporate effort, more advanced inquiries into this matter should be begun and that, in the meantime, all the petitions about the Assumption of the Blessed Virgin Mary into heaven which had been sent to this Apostolic See from the time of Pius IX, our predecessor of happy memory, down to our own days should be gathered together and carefully evaluated.
"And, since we were dealing with a matter of such great moment and of such importance, we considered it opportune to ask all our venerable brethren in the episcopate directly and authoritatively that each of them should make known to us his mind in a formal statement. Hence, on May 1, 1946, we gave them our letter “Deiparae Virginis Mariae,” a letter in which these words are contained: “Do you, venerable brethren, in your outstanding wisdom and prudence, judge that the bodily Assumption of the Blessed Virgin can be proposed and defined as a dogma of faith? Do you, with your clergy and people, desire it?”
“But those whom ‘the Holy Spirit has placed as bishops to rule the Church of God’ gave an almost unanimous affirmative response to both these questions.”
So yeppers, it was a case of Vox Populi, Vox Dei. We did everything but have every Catholic in the world vote on it, or put a gun to the Pope’s head.
In a Holy Year of jubilee right after two world wars, while all the earth was falling under the threat of nuclear war and religion was being killed by Communism, it probably seemed like the best possible time to do it.
Pope Pius XII does say in “Munificentissimus Deus” that he feels that defining the dogma will be “to the advantage of human society”:
“It is to be hoped that all the faithful will be stirred up to a stronger piety toward their heavenly Mother, and that the souls of all those who glory in the Christian name may be moved by the desire of sharing in the unity of Jesus Christ’s Mystical Body and of increasing their love for her who shows her motherly heart to all the members of this august body. And so we may hope that those who meditate upon the glorious example Mary offers us may be more and more convinced of the value of a human life entirely devoted to carrying out the heavenly Father’s will and to bringing good to others. Thus, while the illusory teachings of materialism and the corruption of morals that follows from these teachings threaten to extinguish the light of virtue and to ruin the lives of men by exciting discord among them, in this magnificent way all may see clearly to what a lofty goal our bodies and souls are destined. Finally it is our hope that belief in Mary’s bodily Assumption into heaven will make our belief in our own resurrection stronger and render it more effective…”
So he says that it is being done:
“…for the glory of Almighty God who has lavished his special affection upon the Virgin Mary; for the honor of her Son, the immortal King of the Ages and the Victor over sin and death; for the increase of the glory of that same august Mother; and for the joy and exultation of the entire Church…”
So yeah, it probably wasn’t necessary, per se. But it was a very good thing to do, and God leaned on the popes to do it.