Most wobbly chair legs aren’t a broken joint, they’re a loose one, and wood glue alone often just seeps into a gap that’s too worn to hold anything. Wrapping the tenon in a few strands of wood shim or even waxed dental floss before reassembling gives the glue something to actually grip.
I fixed three dining chairs this way that had been wobbling for over a year, all of them holding steady four months later with regular use. The whole repair took about twenty minutes a chair, including clamp time.
If a chair leg is loose again within a week of a glue-only fix, that’s the sign the joint needs bulking up first, not just more glue.