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> It's been said a thousand times but the ability to produce copyrighted material is not copyright infringement.

Aside from fair use, yes it is.

> If I draw The Simpsons on a piece of paper - whether or not I used AI to create it - it's not copyright infringement.

Only because of the fair use doctrine, which is limited. If it damages the market for the original, then a court could definitely declare it to be infringement.

> Copyright infringement is if I tried to sell that Simpsons work as my own, putting up for consumption and reaping the monetary benefits.

No. Copyright infringement requires neither sale nor misrepresenting a work as one's one. It also covers derivative works, not just perfect duplicates. Copyright covers reproduction and derivate works and distribution/performance -- you can get in trouble for just one of those. Taken strictly, that would be a horrible world, but fortunately the fair use doctrine weakens those quite a bit. On the flip side, if AI reproduction destroys the original markets -- as it is quite obviously doing right now -- then it's going to have a reckoning at some point, given how its legal status is completely based upon getting a free ride by claiming fair use.