It's a little more complicated than how you're making it out to be and it's also going to depend on where you live.

TL/DR: It can be copyrightable as a whole, but the output of a single prompt is not likely copyrightable.

The U.S. Copyright Office put together a report in 2025 on how AI is being handled in the U.S. as well as in other parts of the world.

https://www.copyright.gov/ai/Copyright-and-Artificial-Intelligence-Part-2-Copyrightability-Report.pdf

See Section II - F: “Modifying or Arranging AI-Generated Content”

Generating content with AI is often an initial or intermediate step, and human authorship may be added in the final product. As explained in the AI Registration Guidance, “a human may select or arrange AI-generated material in a sufficiently creative way that ‘the resulting work as a whole constitutes an original work of authorship.’”¹²⁶ A human may also “modify material originally generated by AI technology to such a degree that the modifications meet the standard for copyright protection.”¹²⁷

As several commenters noted, human authors should be able to claim copyright if they select, coordinate, and arrange AI-generated material in a creative way.¹²⁸ This would provide protection for the output as a whole (although not the AI-generated material alone).¹²⁹ A relatively common scenario in registration applications is the combination of human-authored text with AI-generated images. In one early case, for instance, the Office found that the selection and arrangement of AI-generated images with human-authored text in a comic book were protectable as a compilation.

Then if you skip to the conclusion of the report:

As described above, in many circumstances these outputs will be copyrightable in whole or in part—where AI is used as a tool, and where a human has been able to determine the expressive elements they contain. Prompts alone, however, at this stage are unlikely to satisfy those requirements.

If you're curious where your country falls on the spectrum, see Section III - International Approaches.

Edit: added TL/DR.