But yes, a heavier bike in motion at a given speed stores more energy. That's why it's slower to accelerate up to the steady state speed. But I still haven't heard an account of how storing that energy somehow increases speed on the flat road/velodrome in question.
The bike is still the same overall weight. The difference is that mass has been moved from non-rotational areas to rotational areas hence increasing overall mass in rotation thusly rotational increasing inertia.
IOW, it will take more energy to bring the bike up to a given speed but OTOH it will take an equal amount of energy to slow it down as well.
I don't think it has been stated that it would make you faster, it would make it easier to maintain a steady speed on flats and on track (which amounts more or less to the same kind of exercise except perhaps for the sprints).
At the end of the day it's the overall mass in movement that prevails, inertia of the wheel has only a minor impact in the grand scheme of things.
I'd also forward that it may not be to every riders liking. Some like to push constantly, others may enjoy the more even flow of the bike ride being able to just maintain a steady speed at just a minor input.
This allows some to recover from earlier efforts and so on.
Since TS stated his young son prefers to coast downhill I figured he may give this a try. Nothing more, nothing less. No need to analyse everything to pieces: math is one thing people is quite another, right?