It's valuable (think about revenues from tourism) but we still have to live our lives. The ancients built on top of anything was there before. That's why we have so many archeological layers in Rome.
There was an article about this when they were building the tunnel in Istanbul. They did find some significant stuff, but the vast majority of it was stuff they already had tons of. They literally filled warehouses with the stuff, and dumped most of it back in because it was not rare or significant.
Clubbing and nightlife area now, nice place...