> CBP is pretty specific about documentation required to enter the country.
My last flight to Seattle from Mexico a few weeks ago (also, note that I'm an LPR, and not a citizen) I walked up to the CBP immigration counter, looked at a webcam, the officer looked at his computer, said "[my name]?" "Yes." "You're good to go."
I had, of course, my passport and green card on me, but they were held by my side the entire time. He didn't ask for them.