Myself, I'd go rent a Concrete Wet Saw and buy a diamond blade, and slice a neat 1' square out of the concrete slab. Then jack out the old footer, refill with concrete and a steel socket for a wood post.
Or better, a steel socket for a steel mailbox post - you don't have to worry about rot, but cars and trucks do take them off at the dirt every so often, and you don't want to do things over.
For extra credit, you put rebar on the backside of a 9" square of Hot-Rolled Plate and cement that in level and a bit proud of the surface. Then you get a big truck coil spring and tack that down to the steel plate, and mount your mailbox post on another chunk of plate on top of the spring. The mailbox will give a little.
And if the socket gets messed up (or they snap the spring) you can get out the Blue-Point Wrench and fix it. Warm it up to red and massage it back into shape with a cheater bar and a hand sledge. Or slice it off level about 1/2" above grade, and weld on a nice new square piece.
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