I'm bored tonight so I'll play and state my case, all the other comments of which I've read about half be darned! There really is no right answer, just opinions and I find the discussion interesting, as I will the replies, especially the ones I disagree with.
I think, if the shotgun were invented today, it wouldn't be a gauge at all, rather a bore diameter. I think it would approximate the 16 gauge in deference to the waterfowling market and the huge number of people that shoot 16 yard and handicap trap in the U.S. (but then that wouldn't exist without shotguns, so catch 22?) For arguments sake, we'll assume all the uses currently for the shotgun, and all the ammunition, choke, accessory, advancements occur simultaneously with the invention of the scattergun, and everything we know about patterning and wingshooting also occur simultaneously. Shorter shot columns simply throw better patterns per given weight. They are also driven to higher velocities with less pressure in larger diameters per given weight, using faster powders with lower, more efficient charges. Given modern ballistics and components, this could be accomplished in the 16 gauge range, whatever specific bore diameter the engineers settled on. You can fit a useful charge of steel shot (despite non-tox advancements, this is what the vast majority of duck shells still fire), and get a tight 1 1/8oz trap pattern in this bore diameter with rather efficient loads. I think something around 75 caliber would still exist for heavy waterfowl applications and turkeys where a heavier payload is desired. I think a lighter, purpose built upland gun of around 22-24 gauge would exist, and I don't think the .410 would ever be invented.