Well the Exsultet states “O necessary sin” -we agree on the definition of necessary, I think need suits this context just fine. All you’re doing however, is removing the word sin and replacing it with redemption (also necessary, but referenced in a separate verse in the Exsultet)
I understand that you also exclaim Felix Culpa! indeed it is a happy fault, but that’s not all the Exaultet says about the fall.
In any case, the issue was pretty much resolved about 5 years ago on a thread I just found:
forums.catholic-questions.org/showthread.php?t=444694
Essentially what GEddie says is the way that Mormons look at it
I think it may help your understanding, if we put the exultet in context. It is an ancient hymn, sung once a year at the Easter Vigil. On Holy Saturday, after sunset, a holy fire is lighted outside the church which is used to light the Paschal candle. The hymn is sung, in a darkened church, around the Paschal candle. This hymn then opens our celebration of Easter, where we celebrate the Resurrection of Jesus. It is a hymn of worship, where we are worshipping Christ, our risen Lord.
Just as Easter is preceded by Good Friday, where we worship Our Lord at the time of His death. Calling that day Good, when it is a solemn and quiet worship. No music, no bells, no incense. Our shrines are darkened, our water fonts are emptied, our Tabernacles are vacant. What is Good about such a day, when Jesus suffered and died? Our Salvation, is that day and that hour! Good, coming from the innocent torture and death of a sinless and perfect Son.
At the Easter Vigil, we recognize that it was a necessary fault, that brought us so great a redeemer.
This is all one long Paschal liturgy, that lasts three days, and is called the triduum. From Holy Thursday evening to evening prayer on Easter Sunday, you can think of it as one unending worship service.
At no time during the triduum are we worshipping the fault, whether Adam’s, Pontius’ or Judas the betrayer’s. We recognize that God uses both moral good and moral evil to do His Good. We recognize God’s mercy towards His imperfect creation, us. You can think of it as, look at the sinful things we do, and look at God’s mercy towards us. It is, as the popular hymn expresses, an Amazing Grace. You can look at it as, God triumphing over evil. Christ, at His Resurrection, is Triumphant.
Recognizing our sins, and how God reveals Himself as ever merciful, never includes a belief or acknowledgement that God causes, plans, or desires, moral evil. That is 180 degrees outside of what we believe about God’s nature.
Hope that helps.
As for GEddie, he is expressing one theological position. St. Augustine and St. Thomas Aquinas, both venerated, had very different positions on the nature of humans before the fall. Some may seem to you close to Mormonism, but neither one would agree with you that God desired that Adam and Eve would, or as Mormons believe SHOULD sin. The Catholic position on this is firmly, God NEVER desires a moral evil (sin).
This is the position if all of Christendom, from the teachings of the Apostles. So while this “Mormonism isn’t really a Christian religion” tangent, may seem harsh to Mormon ears, it is the truthful fact, that this aspect of Mormonism is well outside of Christianity.