Actually, if one does a border crossing, even intending to travel beyond the Sonoran Free Zone, a passport is not needed. However, an FFM is required, and one's date of entry is entered into an immigration database. And honestly, no matter where I've been in Mexico I've not been asked to produce a passport, and only rarely my FFM. Thankfully crossing in both directions is, to date, and despite the political nonsense afoot, has been seamless. I too am a very frequent visitor to Mexico. Once a week at the very least and for one or two months every winter.
I cross into Mexico several times a month, and spend two months every winter there. I have yet to show my passport even once. I take it with me on long duration trips but that's it. On the one or two occasions I've been stopped (traffic check, military check point, crossing), all I ever show is my driver's license, FMM and proof of auto insurance.