Don't know how common it is... mine came apart when one of my kids decided to sit on it. Your idea will work, but remember it will raise the table height proportionally - make sure that's not an issue when you're seated at the table. I just rotated my round mounting plate a few degrees until there was fresh wood to screw back into and reattached it. The plate covered up the old holes as well - can't even tell I did anything to it.
2014 Dodge Doolie
2002 Cougar 5th Wheel
14' Port-a-bote that goes everywhere with us