It's not obvious at all that we need so much material. That's just one of those weird cascades of misinformation from people playing telephone with the facts...

Dyson originally did some back of the envelope work to see how thick one could be build at 1.0 AU (not a literal solid shell, but an average thickness of a 'shell' of a vast number of habitats and so on) and came up with 3 meters. Sci-fi authors misinterpreted that and started designing vast impractical spherical habitats sort of like a Bernal Sphere but bigger... This was never supported by credible scientists.

The modern conception from Anders Sandberg and Stuart Armstrong as cited by the video is actually of a very thin one, based on another back of envelope calculation: Mercury's metal content. If you disassembled Mercury and made a sphere from its remains (just the metal part), at 0.3 AU, the average thickness would only be about twice that of household aluminum foil.

Except their paper doesn't say why it would need to be even that thick -- they were actually just wildly overestimating to be conservative. Graphene is only a tiny fraction of that thickness. You would need to layer 1000 sheets of graphene to be heavy enough to not be blown away by the sun's light pressure. Or you could have one layer graphene plus 1000 times as much metal.

The result is called a Dyson bubble... Much lighter, and doesn't orbit (so there is no need for a criss-cross pattern) because it is held up by the light pressure.