I used to work at a hot dog joint that did heavy burger business at lunch. We were serving 6:1 burgers; bigger than a McDonald’s standard burger, smaller than a Quarter Pounder. Although they cooked fairly quickly, you’re right, it is still nice to have some waiting in the wings. Instead of just plain water, we used a beef broth. IIRC, it was just a bouillon cube dissolved in hot water.
The steam tray containing the broth and burgers sat at the far reaches of the grill so it stayed warm but didn’t further cook the burgers. It worked great! Only problem was, with an open kitchen, the customers could see the burgers resting in the broth and thought it was grease. They objected, we stopped the practice. If you’re working in a closed kitchen it might work fine.
BTW, I assume you’re talking about par cooked burgers in the water which are then briefly returned to the grill for a warm up before serving.