Inertia of the rotating gearbox components is not a big concern with F1 cars. However, mechanical efficiency of the drivetrain is of concern. As I noted, since 100% of the engine output power must pass thru the drivetrain, even a tiny improvement in efficiency produces large benefits. The typical MT has two gear meshes the power transmits thru. The shift spur gear mesh and the spiral/hypoid gear mesh final drive. The shift spur gear mesh has 99% or better efficiency, and the final drive gear mesh has 98.5% or better efficiency. If you add in all of the other losses from bearings, seals and unloaded shift gears, the input-to-output efficiency of an F1 gearbox is probably better than 98%.
The biggest problem with running the shift gears at higher speeds is the significantly increased viscous/sliding/windage losses. You must remember that in a 2 shaft 7-speed constant mesh MT, at any given time there are over 14 gears, 3 shafts and 6+ bearings spinning, but only 4 gears transmitting power.