A few of the big players are really trying to go down this route, as they feel it offers a real advantage when it comes to offering their staff a good deal, longer hours, better benefits etc.
However, as previous posts have stated, this is not the real answer to the problems within the industry, there are very real difficulties in maintaining quality service, whilst the client's staff are on-site, missed desks/bins etc, not through the fault of the cleaners, but because the clients staff are actually still working, I would assume that the client's staff productivity also falls, during dytime cleaning operations.
However, there are instances, where daytime cleaning can and indeed does work, eg. Hospitals/Airports/Bus Stations etc.
It can also be very useful in large buildings, in order to keep entrances, toilets, corridoors etc cleaned to an acceptable level throughout the day, but my opinion is that the client gets more work done and at a higher quality level by using after hours cleaning, hope this helps, regards,
Rob