Would not sin against a holy infinite God result in an infinite sentence of punishment? And wouldn't limiting the duration of hell diminish the seriousness of sin?

This doctrine was put forth primarily by Augustine five centuries after the church was birthed. This was not a majority view of the early church nor a view that has held a consensus since. It is significant to point out that Augustine was for one, by his own admission, a poor student of Greek and preferred the Latin vulgate of the Scriptures. He is the one who put forth the argument of the meaning of the parallel "aeonios" in Matthew 25. We ought to be more than a little leery of one who came up with new Biblical interpretations who also did not have a handle on the original language of the New Testament. Also Augustine had been heavily into Manichaeism, a type of dualism, before his conversion. His infinite punishment theory for all practical purposes appears to present a very close match to dualism: So according to Augustine, our infinite God of goodness parallels an infinite evil hell where billions of human beings are consigned where they will keep sin, rebellion, hatred for God, and death in existence forever like an open wound in His universe ...never to be healed.

Also God is not only infinite in His being and holiness and justice but He is infinite also in His love since we are told, He IS love. This verse is put forth by John in such a way as to denote that love is His very nature. It would logically have to follow that His love would parallel His being, holiness and justice thereby making all His acts indeed loving ones. I recalled from my childhood the catechism question, "What is God?" I am in utter astonishment. Love is not mentioned in the definition of God in the Westminster Shorter Catechism. I never noticed its absence nor questioned those who taught it to me.

From the Westminster Shorter Catechism
Q. 4. What is God?
A. God is a Spirit, infinite, eternal, and unchangeable, in his being, wisdom, power, holiness, justice, goodness, and truth.

So there you have in part why we contracted this heresy of thinking God's love will not infinitely accompany all His attributes.

Now as far as "diminishing the seriousness of sin" I will put forth two thoughts about this. First, the early church was not "blessed" to have this perspective by Augustine and so therefore did not have its acclaimed power to deter sin as we have been apparently endowed with since. However, any cursory reading of the testimony of the early church shows they ran moral circles around us in every area: in personal holiness, care of the poor, their reputation among the pagans, and their ability to face horrific martyrdom. Here's just a sliver of their testimony within the Roman Empire:

"They are in the flesh, but they do not live after the flesh. They pass their days on earth, but they are citizens of heaven. They love all men, and are persecuted by all. They are assailed by the Jews as foreigners, and are persecuted by the Greeks; yet those who hate them are unable to assign any reason for their hatred." -- Mathetes

Julian "the Apostate," an anti-Christian Roman emperor; A.D. 361-363 made the noteworthy concession, that the heathens did not help even their own brethren in faith; while the Jews never begged, and "the godless Galileans," as he malignantly styled the Christians, supplied not only their own, but even the heathen poor.
(History of the Christian Church, vol. III, p. 50)

I do not think we can make any claims that our more enlightened understanding of our "infinite hell" has been a motivator or catalyst for a more moral Church.

Second, I will assert that the teaching of an infinite hell itself has brought a diminishing of the seriousness of sin. Here's why. When there is an infinitely big stick being held over your head coupled with uncertainty whether you are believing the things that make one safe from the "stick" you tend to be afraid of ALL sticks that come your way. What I am getting at is that fear of an infinitely severe judgement eclipses any ability to process the warnings and real dangers posed to the Church by Christ and His Apostles. Verses like Hebrews 10:30-31: "For the Lord will judge HIS people. It is a fearful thing to fall into the hands of the Living God." and Matthew 25 where Jesus is trying to warn His people of missing the Kingdom, the symptom being the neglect of the "least of these". And our response is to debate the word "aionios".