Thanks for the question.
It is interesting that you should ask a question about the Divine Comedy (for which I am currently taking a course), so it was definitely a fun thing to look at. I think we have to keep in mind that Dante's Comedy is not infallible teaching, but rather meant to teach us important lessons. Dante doesn't actually name the person popularly regarded as Celestine, but for our purposes let's assume it is the correct identification.
I think that Dante has Celestine in Hell because of the grave warning in Revelation against cowardice, and it is a caution against being a coward:
|8 but as for the cowardly, the faithless, the polluted, as for murderers, fornicators, sorcerers, idolaters, and all liars, their lot shall be in the lake that burns with fire and sulphur, which is the second death (Revelation 21:8).
Dante's relevant canto: (taken from this wikipedia article, which mentions the issue toward the end of the post:
vidi e conobbi l'ombra di colui che fece per viltade il gran rifiuto.
("I saw and recognized the shade of him who due to cowardice made the great refusal.")
— Inferno III, 59–60
Because our protagonist, Pietro, eschewed being but in the position of ruling the universal Church, many thought him shrinking away from his duty (essentially cowardice). This controversy followed him for some time, but seems to have been resolved in the subsequent investigation which led to his canonization (done in a much cruder vote than with today's standards).
I find it understandable that Pietro didn't want the job. He sought a contemplative life, had entered a monastic order, a branch following the rule of St. Benedict, and may very well have taken a vow against positions of authority. He was virtually strong armed into the position. His desire to resume a monastic life ultimately ended in prison instead. The politics seemed to outweigh the inner calling, at least for those in power. He was vindicated and so I think we have to give him the benefit of the doubt.
Only today I listened to an interesting podcast on Pope Francis and a criticism leveled by Archbishop Vigano as the Jesuit having broken a vow. Like other religious orders, the Jesuits have a strong vow to not take any position or office under pain of mortal sin, unless they be ordered to by the superior of the order or the Pope himself. Jorge Bergoglio was never given an order to take such a position, and in becoming a Jesuit he would have had to take a vow promising to resist and refuse any such office.
You can listen to that below. (I think it may cast some light on the mind set of Pietro, who wanted to stay true to his personal calling and maybe even a vow)