Having it mounted to the hatch as well as the bumper would take a lot of wobble out of a tire carrier. I thought about that but wanted to be able to quickly open the hatch while on the trail or camping. There is also a lot of movement in the end of the frame. I usually go on the expedition type trips with a buddy who usually sets up or breaks camp in about 10 minutes. Even with easy access, it still takes me about three times that long. My tire carrier doesn't wobble very much compared to most, but I use a bolt instead of a latch to lock the swing-outs down to the bumper. 1/2" bolt, just like a whole bunch of my suspension components with the ratchet wrench in the driver door pocket. The swing-outs used to have brass bushings, but I got tired of fighting it as it was always too tight or too loose. I redid it over the first COVID lockdown to add the traditional 1500 pound trailer spindles and bearings. Having the ends bolted down takes the strain off the trailer spindles.
With the fold down tables, my Coleman two burner camp stove fits perfectly on the tire carrier side (not the gas can side for obvious reasons).