IIRC there was a protective limestone layer with a gold cap (removed for use in other buildings by later civilizations) on top of the pyramids versus leaving them as is, they originally did not look like unfinished stone. There is constant wind erosion on the exposed stone layer now. I don't know what a good solution to this now.

I think it would be cool to imagine ourselves as part of the process of civilization that created these buildings and restore them to their former glory. If the Mona Lisa was ripped in half we would surely restore it back to a single piece. Why should we not rebuild ancient Rome and host pop-up shops and events in the Forum?

It is an interesting thought, but I think your example doesn't work. In that we have two complete halves in need of minor repair. For ruins, we have parts left, and don't really even know for sure what it's supposed to look like. I mean, a very good idea, but not for sure.

And especially, over time, you can end up with a bit of a ship of theseus.

Also interesting -- if some day one of the earthquakes there knocks down part of the colosseum, will we rebuild the ruins to their ruinous state?

You know, for grain storage, and for the ancient aliens to communicate through crystal power, or a flooded Bass Pro shop.