It is happening today. Chambers inside Egypt's great pyramid were detected in 2016 using muon imaging. It was a slow process but radically less damaging than the alternatives such as drilling test holes. More commonly, ground penetrating radar is regularly used to avoid digging test or exploratory trenches across sites. As resolution increases, fewer and fewer trenches need be dug. Scans are often used years prior to digging as a non-invasive way to confirm the existance of structures in aid of grant proposals. At some point, the scans will be the entire dig.
I've heard of that application, but will it detect faint writing, which experts weren't intially sure was writing, on a 4 cm long piece of rock? I don't that's happening any time soon.