The Utopia Degeneracy Question

Humanity repeats itself in waves. Nothing really changes.

Yes, and no. I'd like to think each time the cycle cycles we come around with a slightly different understanding.

Nope, things have not changed and that is why relational events in the Bible still apply even today. I see it as waves that go up and down. Things get good, everyone gets bored and it goes back to bad which then they slowly struggle to make it good again. So, yes it is a cycle, but nothing changes.

Why can't change and changelessness exist in the same universe? Many aspects of God and his/her creation is a mystery. Seeming paradox make sense to me in such a context.

You should read about the pride cycle that the Book of Mormon describes. When people are prospering, they tend to grow complacent and prideful, and do forget their God. It often takes new hardships and crisis to humble them, and remind them of their dependence upon God. American history alone has gone through the pride cycle a few times.

I'm not much into following any one particular religion but I do like this concept as it does allude to a spiritual truth of sorts.

Most of the world religions descend from syncretism: One objective standard of truth, mixed with local man's errors. For example, a lot of cultures have a legend of a Flood, followed by the construction of a great tower and the scattering of mankind. The Taoist Yin-Yang teaching is very similar to what the Book of Mormon teaches about there needing to be an opposition in all things(2nd Nephi 2). And, of course, most religions teach human decency, faith in a higher power, purpose to Creation, and the promise of a better afterlife.