It's literally in the constitution:

> [the United States Congress shall have power] 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.

https://en.wikipedia.org/wiki/Copyright_Clause

It literally predates the United States Constitution by hundreds of years: https://en.wikipedia.org/wiki/History_of_copyright

Also, I'd be careful at taking the reasoning of political documents at face value. Many items in the Constitution are post-hoc, Lockeian/liberal justifications for a social order that was in fact largely copied over wholesale from English parliamentary monarchy, with surprisingly few tweaks.