Stephen
...don't I know you....?
I guess a lot depends....again....on the company and size of building. I know some big companies that will have day cleaners but their tasks are more maintenance. They will have to maintain the washrooms/toilets, replenishment, staff kitchens (not industrial), drinks machines, bins/waste and basically general mopping up during the day. When you have huge buildings to cover you rarely get time to do the usual cleaning rounds since there is much more that needs doing.
You've certainly hit the nail on the head with your comment, Stephen, women do prefer the unsocial hours due to other commitments...family. The reason for some companies prefering the cleaning being done during the day could be due to their insurance companies requesting it.....obvious reasons, or it could be a company was previously 'stung' by a cleaning company and prefer not to take that risk again.
I have to say I prefer the late night method - generally there is no one around and you can, often, take as long as you like without 'busting ya gut' to get it completed before the arrival of morning staff.