This is a good question for highlighting various assumptions around God's purpose for humanity and the terms we associate with it like "perfection" and "character".
To begin, defining "perfect character" as impeccability is a negative way of defining a perfection and is a difficult assumption to begin with. It's a bit like saying someone is a perfect driver because they don't have the ability to break driving laws! Surely that can't be the case... Imagine the stereotypically meticulous German man driving 321 km/h (200 mph) down the autobahn (where there are no speed limits). I don't suppose anyone would regard his driving as "perfect" let alone "ok"-- he'd more likely be considered reckless, at best. Nevertheless, he would not be breaking the law of the autobahn! It seems defining perfections negatively is not so helpful.
In the same way, perfection in humans should not be defined negatively. With that in mind, we find that the Bible gives us positive hints at what perfected humanity looks like, not a stark definition. Perfected humanity is described (not defined!) as a mystical state involving new bodies and souls (with new abilities/senses), along with mysterious knowledge and ecstasies we cannot currently comprehend. (1 Corinthians 15:35-58)
And we receive a glimpse of this new state when Jesus "the first born among many" (Romans 8:29) who resurrects and reveals Himself to the disciples. Alongside these positive attributes, we are also told that we will be impeccable but it is not the purpose of our salvation. The purpose of bringing the Israelites out of Egypt was so that they could go to the promised land (not just wander around). And now again, God's people are being brought out of their sin, and being called into the True Promised Land—the new Heavens and new Earth, and unrestricted knowledge of God.
And so, if the purpose was always to have intimate knowledge of God with these incredible bodies, it's much more relevant to ask the question "Why did God make incomplete humans?" Rather than "Why didn't God make humanity impeccable?" But for the moment, I'll put off this new question and will try to answer the original question through a quick summary of the paper "Can God create humans with free will who never commit evil?".
- God and His attributes are one.
- No other beings fully share in any of God's attributes.
- One attribute of God is impeccability.
- Therefore, for a being to be impeccable, implies that being is God.
- Anything created by God is not God.
- Humans were created by God.
- Therefore, humans are not impeccable.
Returning to the question, it seems to imply the primary purpose of godly character is impeccability, whereas the primary goal God had in creating Humanity was so that they would grow in their knowledge and experience of Him. God has always had an eternal plan for humanity, one in which we are forever learning deeper mysteries and experiencing ecstasies beyond current comprehension.
The first picture we get of this is cultivation. Adam was tasked with working the garden and making the whole Earth like it. He was supposed to cultivate the unfertile dirt into rich soil and abundant greenery, just as he was tasked to cultivate his soul and relationship with God. And this work was made so that he would become perfect along with all of creation under his sinless rule. Those mysterious bodies and new Heaven/Earth were originally part of the plan for Adam!
But he forfeited that path and chose death. Which prompted the incarnation and humanity's redemption back to that plan:
8 To me, though I am the very least of all the saints, this grace was given, to preach to the Gentiles the unsearchable riches of Christ, 9 and to bring to light for everyone what is the plan of the mystery hidden for ages in God, who created all things, 10 so that through the church the manifold wisdom of God might now be made known to the rulers and authorities in the heavenly places. 11 This was according to the eternal purpose that he has realized in Christ Jesus our Lord, (Ephesians 3:8-11)
14 For this reason I bow my knees before the Father, 15 from whom every family in heaven and on earth is named, 16 that according to the riches of his glory he may grant you to be strengthened with power through his Spirit in your inner being, 17 so that Christ may dwell in your hearts through faith—that you, being rooted and grounded in love, 18 may have strength to comprehend with all the saints what is the breadth and length and height and depth, 19 and to know the love of Christ that surpasses knowledge, that you may be filled with all the fullness of God. 20 Now to him who is able to do far more abundantly than all that we ask or think, according to the power at work within us, 21 to him be glory in the church and in Christ Jesus throughout all generations, forever and ever. Amen. (Ephesians 3:14-21)
So at the small snapshot we get of humanity's first temptation, we should find ourselves asking something like "Will Adam and Eve trust God's first commandments, and therefore learn more of His Wisdom: how to live in the world He has made? Or will they reject His wisdom and decide to live on their own terms?"
This might prompt someone to ask "Why would God make incomplete humans that need to grow in their knowledge and experience of Him?"
And that is simple: because He is Eternal and we, His creatures, are not.
Without an eternal plan, how else could a finite creature grow into their knowledge of The Absolutely Infinite and Eternal Being? We have to learn simply at first, just like how parents teach and raise their children with oversimplified and "safe" explanations. So God gave us only a few commandments and free will so that we could grow to be more like Him in due time. In a silly way, He is basically onboarding us into our existence.
But then one might ask "If humans are not impeccable, how could these new resurrected bodies be impeccable when they are still human?" And that is addressed by the mystery of marriage.
31 “For this reason a man will leave his father and mother and be united to his wife, and the two will become one flesh.” 32 This is a profound mystery—but I am talking about Christ and the church. (Ephesians 5:31-32)
Just like how God used the Israelites to give a picture of the spiritual exodus of his elect out of their sin, so too did He make marriage so that it would point us to the spiritual reality of our union with Him in Eternity. The Church is Christ's bride and will for Eternity grow into Oneness with Him.
And if you asked me, I think we've married up...I wonder if that means He has impeccable taste? ;)