From what I understand, if people try not to allow cleaning staff into the rooms it can be in a conflict of interest for the hotel management from what is best for all guests - [in case there is a situation that needs attending] - so I appreciate when a hotel makes daily checks in each room.
Also - I am surmising that the cleaning staff may be paid 'per room', and that when you don't let them in to clean, they don't get paid??
The only time I didn't have cleaning staff in was when I was horribly sick with a bad cold/migraine a couple of years ago for a couple of days. (UGH!) I told them so, asked that they provide clean towels, while I gave them back the towels that needed replacing, and I provided our garbage bags for them, and they gave me fresh ones. To be honest, I really did NOT want to make them sick and catch my cold/flu! I don't think that's fair to them at all.
At least they were able to see me though, 'check in' with me, and it all makes me feel safer, overall. This was at Hojo's.
With the in-room safes (HUGE!) at Hojo's there was no reason for us not to let them in. I always have photographs of all items packed in my suitcase, that I reserve on the camera SD card, which I hold onto in case our luggage goes missing on the airlines. I seriously doubt anyone from housekeeping would ever go through my things - at least, not at Hojo's! We had left the safe open once with valuables, on Oct. 2009, (by accident and all was well) and we have met the same house keeper 2 consecutive years in a row (she was the one cleaning our room) so obviously, hotels that take good care of their staff care enough to pay them enough to want to be there. Very nice, personable staff, I feel like I know them. Hojo's really is our second home.
I am currently ordering Avon products for the Hojo housekeeping staff to 'tip' them with unique items on our next trip; maybe Aero chocolate bars (available only in Canada I have heard from these boards) will also be part of the daily 'tip.' We do leave cash sometimes as well, but also feel that special small-sized gifts are nice for them to receive.