It's certainly a stupid idea if your trying to illuminate at the suns level, but if you wanted an area to have permanent moonlight? Not so unreasonable.
The moon is 400,000 times dimmer, so 1km^2 of mirror, which is ridiculous, could illuminate an area the size of Germany.
New York metro area is 12,000km^2, which would only need a mirror 173m on each side.
Actually might not be a bad tourist attraction for a crazy city, permanent artificial moonlight.
While it would be cool for it to appear the size of the moon, it is not necessary with a shaped mirror.
You can keep the same size in a higher orbit, maybe even geosynchronous, then sync the rotation of the mirror to keep it pointing in the same spot on earth.
Granted a shaped mirror that size would be much harder to put into orbit than a flat mirror.