You are asking finite mortal minds to understand God’s mind - that is impossible.
But let me convey some personal insight that might get you started on a path to greater revelation.
Turn this question around and ask “Why did God lower himself to the stature of humanity and permit evil men to put Him on the cross to be cruelly tortured, abused and killed?” Clearly, God could have just appeared on earth and said “enough - I ban all sin and evil”. But no, He did not do that. He, for reasons not fully understood to us elected to identify with us and share in our suffering human condition. He set an example. He essentially said “see, I take on the same hardships and suffering that you have and take your penalty onto myself as an act of love”.
God did not grant Himself an exemption to our human condition or suffering that humanity “deserved” as a result of its original disobedience. Jesus did what all true leaders do by empathizing with His people. He asked for no more of others than He Himself was willing to do in our stead. Further - Jesus took on one of the worst forms of torture and death imaginable - the Romans were experts in administering pain and agony to teach lessons to those who would be so bold to disobey their rule. But God also put His son Jesus through a deeper passion of spiritual agony that we will never fully know by imparting the penalty of all of humanity’s sin on His beloved Son. So in addition to terrible physical suffering (that the others crucified with him suffered in similar form) Jesus also suffered infinitely more than any human can imagine or ever know by suffered both severe physical and spiritual pain at an unimaginable level that only the Divine can suffer through the human soul of Jesus.
Can you imagine the spiritual agony the Divine Jesus suffered, as the incarnate 2nd person of God who is hypo-statically united through Jesus was mysteriously abandoned (veiled) by God the Father momentarily on the cross when Jesus cried out “My God My God why have You abandoned me”? How Jesus could not despair in that moment and still have perfect faith to even call on God is beyond comprehension. We humans just can’t possibly fathom that level of spiritual pain for Jesus as Son nor God the Father in permitting it happen for love of humanity. On the cross, God put 100% of His Love on the line for Humanity and made us equal to Jesus’ humanity. That is profound love and empathy.
My own conjecture is that God elected to use the pain and suffering of the crucifixation since it released the highest and best grace for all of Creation. There is something spiritually necessary that we can’t quite fathom that probably relates to God’s Justice (with real eternal rewards or penalties and consequences) as well as for settling spiritual Divine debts (with Satan). After-all - God could just annihilate Satan and instantly preserve us all from original sin if He chose too - but He does not. That would not be consistent with His Justice.
Note too that the selfless act on the cross makes it possible for humans to RELATE to God’s love through empathy with things we can understand (pain, selfless sacrifice for others, the Father’s loss of His only son, injustice is making an innocent person pay for somone else’s faults etc.). We are sensual as well as spiritual beings - we can see God suffering through Jesus on the cross and love and have sorrow for that act. We could not love God as much if He just popped down and said “here is a free pass to heaven”. He wants us to cooperate with Him as a partner so that we can share in His Glory. This is what is profound - God wants us to not just be saved but to participate with Him and share in the love, glory and satisfaction of that salvation by suffering right along with Him.
This act on the cross becomes a mechanism for opening up humanity’s heart to LOVE. We see an innocent man dieing for us and because of us. How can we not love such an act? Yes some won’t still…
Jesus had NOTHING to gain for himself personally (on earth) in dieing on that cross other than His being unconditionally obedient to God’s will. Jesus gave us all the model for expressing perfect selfless love - sacrificing one’s own comforts and laying down one’s life for our fellows.
Now consider that there is perhaps some supernatural and divine mystery associated with suffering and passion that we can not fully understand at this time. Consider the nature of suffering. I am sure you can recall unpleasant times in your life - perhaps you were hurt, injured, insulted, harmed or even just cold from being exposed to the elements. Flash forward to a better time when you were past it or overcame it. You might be able to recollect a general accounting of the suffering but unless you are still suffering that pain - its gone and is just a memory. We likely do not dwell on it - its often forgotten and in its place we are shaped by that experience and stronger of character for having endured it and beaten it. There is even a strange sense of accomplishment and overcoming that prior pain and suffering.
So, no doubt there are many dimensions, too many to comprehend as to “why” God opted to use “suffering” as consequence for disobedience. But the thing this is most profound here is that by humanity disobeying, God still had a plan to rescue us from our poor choices. God can’t fail. The ironic thing is that by humanity’s disobeying a GREATER GOOD that had we not sinned comes out in the end for those who choose to trust God the 2nd time around (the first was Adam and Eve’s choice). The difference from the original estate if obedience is that the greater good requires that we humans suffer as a result of God’s Justice.
I’d say only a fool would not trust God this 2nd after seeing that He lowered Himself to human estate to show us the way back to Himself and how to love Him in the way that pleases Him.
Hope this helps some,