The trees are an interesting touch, but this seems like it misses out on the greatest active benefit of having a glass roof for a church: having natural sunlight fill the pews when services are held on nice days.
The problem with filling the interior of the cathedral with light is that you won't get the same effect from the stained glass windows and the candles. The great thing about this design is that it leaves the traditional experience of the interior of Notre Dame exactly the same while also offering a new space for contemplation.
Sunlight may be explicitly unwanted since strong light tends to cause a lot of things to decay more quickly and the church presumably has a lot of fragile antiques in it.
The surviving inner structure would block the light anyway. The same structure that stopped the roof falling into the building too much.