The two big problems most people have with religion are evolution, and the problem of evil as you describe it. There is only one rational or logical solution to the problem of evil in the world: Evil exists in the world because neither God nor anything or anybody else has any power over it. The term allmighty or all-powerful means having all the power that there actually is, and not all the power that anybody could imagine. God is all powerful in the realm he inhabits but God and the spirit world have very limited if any power to act in this physical realm which WE inhabit.
That’s an interesting perspective. As for me, I understand God to be omnipotent—all-powerful. But He chose to give human beings (and angels) free will, because He created us to love and to worship Him. Love and worship cannot be genuine unless they are freely chosen, and to be freely chosen, there must be an option to choose to love and to worship what is other than God. To choose other than God is to choose evil, and to choose evil is to sin. Sin brings into the world natural consequences, because it violates the principles of the natural and/or moral orders, and causes, as a result, suffering — suffering not only for ourselves, but also for others.
Evil exists in the world because of free will. Lucifer is only the temporary prince of this world. God’s will cannot be confined to human logic or rational thinking.