TN - from a practical standpoint, owning all 12 gauges has some merit though you'll still likely need different loads for deer, waterfowl, trap, turkey, and upland game so the net gain may not be what you hoped for. Many of us like different firearms and shooting them, so one or more of each in 12, 16, 20, 28, 410 is rather appealing. Plus a couple extra boxes of 20 gauge shells is not a big deal.
Also consider getting your Mrs/Significant other/kids (if applicable) in the sport to spend time outdoors. For new shooters a 20 is easier to manage than a 12 gauge.