I think "bright" is relative. There are plenty of limestone structures in the world, including some modern-built pyramids (of much less grand scale). Limestone is soft and porous and will never glisten the way marble does.
It would have been very impressive, to be sure. But I don't think it's going to match the experience you have in mind.
Since any such modern facing would completely hide all of the authentic material, you might as well just build a completely modern structure elsewhere. With modern building techniques it wouldn't take all that long.
That would actually be a pretty amazing thing to recreate the pyramids relatively close by as modern structures and replicate it so people could experience everything in it.
There's not really anything inside a pyramid. It's just a pile of rocks. There are a few chambers, but you don't need the entire pile of rocks for people to experience those.
If you want to stand inside a big pyramid shape made of modern materials, you can go to Las Vegas. From inside it looks like any other building, though I suppose the rooms with the slanting windows are faintly neat.
So the outer sides of the pyramid are these very precise steps with amazing accurancy, and it's just filled in (where there aren't chambers) with... piles of rocks?
I've wondered if you could build a stone pyramid -- using modern machinery -- financed as a time capsule.
For $X dollars, you can pay to have a cubic foot of stuff interred in the pyramid, for future historians to find. If a pyramid-sized pyramid can hold Y such lots, can you sell enough to pay for the construction?
It doesn't have to be anywhere specific, just pick a spot that's relatively dry and has appropriate stone nearby. Run it as a tourist trap afterwards to pay for whatever ongoing costs are needed to keep people from disassembling it for raw materials.
> Limestone is soft and porous and will never glisten the way marble does.
It was polished fine limestone, though. Maybe it wouldn't have had the same optical qualities as polished marble, but it could [in theory] easily have been incredibly bright with a high reflectance. Modern polished limestone can have a strong gloss almost indistinguishable from polished marble, but maybe that's from modern sealants, polishers, or power tools?
It would have been very impressive, to be sure. But I don't think it's going to match the experience you have in mind.
Since any such modern facing would completely hide all of the authentic material, you might as well just build a completely modern structure elsewhere. With modern building techniques it wouldn't take all that long.