Yes, this is my exact issue with some framing of AI. Creative people love their influences to the point you can ask them and they will point to parts that they reference or nudged to an influence they partially credit to getting to that result. It's also extremely normal that when you make something new, you brainstorm and analyze any kind of material (copyrighted or not) you can find that gives the same feelings you desire to create. As is ironically said to give comfort to starting creatives that it's okay to be inspired by others: "Good artists copy, great artists steal."

And often people very anti AI don't see an issue with this, yet it is in essence the same as the AI does, which is to detach the work from the ideas it was built on, and then re-using those ideas. And just like anyone who has the ability to create has the ability to plagiarize or infringe, so does the AI. As human users of AI we must be the ones to ethically guide it away from that (Since it can't do that itself), just like you would not copy-paste your influences into a new human made work.