A world with no evil means that either God constantly intervenes to prevent evil from happening, or mankind is incapable of committing acts that are evil. Either way, man has no free will.
It doesn’t hold either that God could give us “mostly” free will, only preventing the “really bad stuff”, such as Hitler and Stalin’s mass murders, because where is the line drawn at which point something isn’t “really bad”? Is the murder of one million people “really bad”? What about one thousand? One hundred? One? Should it be that He intervenes only when human life is lost? Well, what about rape or torture? These may not involve death, but are clearly evil. So you can’t even reduce it to “only when someone is physically hurt”, because psychological damage from verbal abuse or other traumatic events can deeply affect the quality of a person’s life. It’s a slippery slope that, in the end, equates to man’s being prevented from committing evil acts.
God wants mankind to love Him and seek a relationship with Him, but he wants us to choose to do so, not to be coerced into it.