Why not have the gears inside the bottom bracket?
The lack of popularity is partially because it's a solution in need of a problem.  The effect of rotating mass in general is generally overstated when considering the total energy that goes into cycling, and mass near the axle has even less of an effect.  You can work out the math here.

The main advantage comes when considering unsprung mass on full-suspension bikes, where having weight on the rider's side of the suspension can improve the handling and response of the bike. This is why inroads have been made in downhill circles.