Some Thoughts on Incompatibility Principles: Part 1

I want to take this post as an opportunity to get some ideas on a few different thoughts that I have been having about incompatibility principles. Incompatibility principles are propositions that claim that God and evil are incompatible on some level. Every argument from evil needs one. There are of course many different types of incompatibility principles, but the hands down two most famous ones are "If God exists, then evil does not exist" and "If God exists, then gratuitous evil does not exist." Given the failure of the logical problem of evil, this post will not deal with the former.