This presumes that there ever comes a day when a non-compliant DL really is unacceptable for travel (let's just pretend), I would still travel with the DL because I always carry it. I also have a passport book, passport card, and GE card. I travel with the passport card and have the passport book (& GE as backup) for international.
It is always good to have a secondary piece of IDand the passport card only costs $25 above the passport book fee.
But, this is nothing to worry about yet.