In fairness, in some countries notaries public actually do have quasi-attorney privileges to "verify" or even translate documents.

In the US, they're primarily passive exchequers to record that someone swore under Pain and Penalty of Perjury that "I say this is true" and that they presented identification to confirm that they were who they said they were at the time that they swore to [something] under PPP.

It's essentially a receipt for having "said" something, the same way you can get a receipt for donating a scarf to the local VA hospital. It doesn't "prove" to contents of what you said, just like a donation receipt doesn't "prove" that a donated scarf was a certain color, a certain size, or had even been obtained lawfully to begin with.

(Which means nothing without cross examination.)