I assume the workers are paid hourly, so wouldn't the cost be the same? Are second and third shifts more costly?
It might not even be necessary to work 24/7. My street was recently dug up over its entire length to install new water mains and sewage pipes. It took nearly 2 years. Only 1 crew of some 5 people were working on it at any given time. Given that the street is roughly 1km in length, at least some of the work could probably have been done in parallel with multiple crews.
But that's just my armchair constructioning.
This is routine in Asia. Just look at this video remodeling a railway station in just a few hours [1].
For that to work though, the construction companies need to have the backing of the government that there will always be budget to keep these people employed - even for supposedly "low skill" work such as road construction, recruiting and onboarding costs are significant. But when government appears to be in budget crisis to everyone reading a newspaper, no reasonable construction company will hire more workers than they could also use for private projects (e.g. home construction, garden remodelings, ...) if the government decides to undergo yet another shutdown.
Also in evenings, road crews have extra safety precautions (there’s a higher chance of running one over in the dark) and that’s labor too.
It was an eye opener for me, it had never occurred to me that such late night roadworks was carried out to reduce daytime disruption to traffic.
There again, this is in a city that is currently expanding the district heating system that they installed when they built a new waste incinerator - so that the process of waste is: 'burn the waste, heat water to turn turbines to generate electricity, the waste steam is then fed through pipes in the city to hospitals, council owned buildings, and some select high rise apartments, then the water is returned to the incinerator building to be reused. Solid remaining 'slag' from the burnt waste is used to make non-fossil asphalt. And the incinerator building also has wind turbines and solar panels covering the roof.
At least for Germany, yes - by law, night and weekend/holiday work must both be approved by the authorities and compensated. Most union contracts here go way beyond the vague notion of the law and require significant compensation.