The actual text of the US constitution maybe?

Article I Section 8 Enumerated Powers Clause 8 Intellectual Property

        To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries;

Seems like the idea is to promote innovation by making sure it is for a limited time only seems pretty ingrained in the idea.

If it says 'for a limited time', then wouldn't tying itmto the lifetime of the author be unconstitutional? Because strictly speaking it's impossible to predict whether an author's life will end.

It's in fact trivially easy to predict whether an author's life will end.

Watch: I predict an author's life will end. I give it very high odds indeed.

Corporations can hold copyright and can be undying.

If the author is a real person, it's life of the author plus. If it is a corporation it is a fixed amount of time.

Decided in Eldred v. Ashcroft. As long as Congress stipulates a non-infinite copyright term, it's constitutional. Given that the chance of a human being eventually ceasing to live has been 100% so far, it's legitimate to assume that life + n years is still a finite period of time.

"Progress of Science and useful Arts" isn't utilitarian in the sense "benefit society as a whole".

For Americans, the utilitarian argument is made in the Constitution:

_"The Congress shall have Power To lay and collect Taxes, Duties, Imposts and Excises [...] to promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries"_ [1]

[1] https://constitution.congress.gov/constitution/

Doesn't say anything about "benefit society as a whole".

Because that's the stated purpose of patents in the US constitution.