In the future, maybe there will be a more efficient mechanism to pre-scan a construction site for noteworthy finds. I'm imagining a non-invasive deployment of cyber-worms that go thru soil & nano-drillbots that go rock to survey a site. With sufficiently advanced sensors (which totally exist in my sci-fi future), you could pre-find all the cool stuff. When a construction site has been blessed as 100% uninteresting, you can blast away with your explosives with reckless abandon. You could even buy archaeology insurance to cover you in the event that construction efforts unveil something this survey missed.

Can anyone familiar with construction comment on how construction sites are blessed now, and what hedges are available to construction companies who have to halt construction because someone found dinosaur eggs?

Construction in Italy, especially in Rome, is regularly stopped because they hit something old -- old meaning Roman period. The same is true about other ancient cities such as London and Jerusalem.