Why fuel left/right when C172 is secured?
It's pretty much to limit imbalance when parked on a slope, and if the tanks are full, stop fuel from the high side tank from forcing fuel out of the low side tank's vent or seeping out the fuel cap if it isn't completely fluid tight.

On the '68 Cardinal I used to own, the vents went straight to the wing tip on each tank's side.  If parked on a side slope with fuel on both and full tanks, you might end up with a third of the high side's tank volume on the ground under the left wing tip (later they were cross vented to prevent this).