Not if you're persistently using it for multi-week sleep deprivation operation to "soften up" an area before attacking.
Moreover, the Sun's illuminance is about 1kW/m2 around Earth. 10000×60m2 satellite will thetefore intercept 600MW, so that's 260W/m2 on the focussed area. You're not going to burn anything with that.
Heck, I haven’t done the math or anything but I bet even if you did instead use parabolic reflectors that were tuned to focus at the earth’s surface, it would still be very difficult to keep them aimed at a specific point for long enough to achieve significant heating. I wouldn’t be surprised if it’s difficult to achieve an increase in heating that’s close to, say, the heating difference from standing outside at noon as opposed to 5PM. Which then doesn’t do much because you couldn’t effectively use a reflector at noon, anyway. You’d want a lens instead. Or some sort of complicated Newtonian telescope type contraption.
This honestly strikes me as an innocent test of one random idea/technology. The whole "conspiracy level" thing (if it were to ever happen at all) would come later on, and most likely from entirely different people usin' the things discovered from experiments like this one in wholly unacceptable ways because they simply have too much power, money, and time, and not nearly enough good sense between their ears.
Sad though that as other folk have pointed out, if the technology were to work as expected, then it could also be used to help mitigate global warming by reflecting a specific amount of sunlight away from Earth, too. The sad part is that's likely not what such experiments will lead to initially. The "bad people" tend to be pretty quick to try to weaponize or monetize (or both) anything they take an interest in.
And a satellite isn't going to provide "hours" of extra light unless it's a very much higher orbit than current proposals. At 600 km altitude, you're talking 20-30 minutes even with an unbounded number of satellites (and 10-15 minutes when you've only got a few satellites). Same reason as sunset itself happens: Earth just gets in the way.
If this is somehow an actual problem, it is far more solvable with tethered blimps or drones, battery pack in a container on a truck, a spool of wire, and light banks as big as you want. AND that isn't subject to clouds (but would be subject to high winds, which would also be more likely to cancel/postpone the event than clouds).
Meanwhile, they go beyond the already massive disturbance of existing terrestrial lighting and overwhelmingly screw up the biologically critical light signals used by every plant, insect, animal, and human in the zone, and do it at multi-kilometer scale.
Edit: Even if the revenue potential is actually huge, it is no justification. For any intelligent person, the actual sponsorship message will be "Tonight's lighting brought to you by [Insert_Company_From_Which_I_Will_Never_Buy_Anything_Again]
This level of stupidity is beyond evil — the kind of lunacy to make a good argument that humans should not exist.
I saw a presentation by one of the founders where he talked about several use cases where the benefit is just phenomenal.
They don't fool me for a second, however. The end goal of this is to build a weapon that can fry people/places on demand (but only the bad guys, of course).
The military application would just be illumination.
I'm sure that's attainable with a few hundred sats.
Can someone do the math?
Are bullets better than knives?
Each thing has its own place.
Like this, for example.