Would splitting humans into two groups, those that work and live during the night, and those that work and live during the day, help the economy in any way? What would be other considerations of organizing society this way?
Capital expenditure could be greatly reduced, allowing more money to be spent on other things.
"If we spend less up front on X, then we can instead invest in Y, and allow greater growth in other economic sectors"
This really comes down to social efficiencies. How much good can come out of spending on the needs of society, or flipped: How much better can we use public services we've spent money on if we change how we use them.
Consider transit: Moving everyone around a city specifically for 9-5 jobs costs a LOT. To the point where there are major efforts to encourage spreading start/stop times around more so that fewer people get trapped in 'rush hours' - If the subway is packed to being 50% over capacity at 7:30am, but completely empty at 2:00am, then that represents a horrible imbalance and unused capacity...
We could build a second subway to meet the needs of transit at 7:30am, spending vast amounts of capital to do so, or we could shift half of the 7:30am demand to another time slot, and suddenly both times are back down to using a mere 75% of capacity without having spent a dime on new infrastructure.
This could be expanded to businesses as well. You could have an office that fit 50 workers for X cost. To expand that to 100 workers you could spend roughly X again for a similar space and equipment and have everyone work the same hours... But since your workers aren't actually using that existing space 24/7 anyway, why not save costs and spend much less to retrofit the existing space for "Hot Desks", where the day shift packs their stuff away in the afternoon, and the night shift then comes along to unpack their stuff and use the same chairs and desks?
Some time ago I toyed with the idea of an ultimate sweat shop - shared beds, shared baths, shared work spaces, and so on. Everything is used 24/7 (with some spares to allow for maintenance and repairs). People sleep 8 hours per day, rest 8 hours per day and work 8 hours per day. That would divide people into three separate groups - day sleepers, evening sleepers, late sleepers. You'd need one third the living space, one third the office space, one third the amenities. Which obviously saves some money. The owners of such sweat shops might profit, the economy as a whole can concentrate more resources on other tasks (war, leaving the planet, or whatever else might make people choose such drastic methods), and the environment might also profit. For the people, it would be close to hell, though. And we obviously wouldn't get a consumer driven economy - the economy would only grow for the owners and/or the governments of such a society, in terms of what they can do with all the cheap manpower.
One way it could be good for the economy (and bad for people) would be to have the two groups competing. Reward which ever group does better on various metrics like widgets produced, crime, pollution, etc. Try to get the people mad at each other rather than the government for the long hours they have to work.
On the other hand, the Soviets tried something similar to do away with weekends. This economic and social experiment was regarded as a failure. What you suggest would be even more extreme and thus fail even more.
I'm pretty sure that the night/day model has been used in stories before. Dystopia, of course.
It think it might be wash in most sectors, except factory’s and such which already do this and mostly in 4 day intervals. But this split might mean you need half as many restaurants, post offices, dmvs, grocery stores, and office space but they would have to be open 24 hours, if you had half of kids go to school during the day and night, you would need day/night teachers and staff, and day/night child care. Many jobs require daylight, even the stock market closes at 4.
Would producing things 24 hours help the economy?
All history proof says YES. Mines working on 3 shift mine resources all the time. Steelworks produce things all the time. Machine shops refine those things.
Service industry is booming because they serve people 5 times (or 7) instead of regular three.
What you need to remember is to leave some room for people.
For example forcing strict 12 hours shift will leave people working for owners profits but not able to spend their earn money. So if your economy is not based on extortion and export then you may find yourself in a bottleneck where people would just not be able to return earned money to economy.