For some properties yes, for others no. The penny pinching to place "decline service" cards just makes the policy confusing and convoluted.
If they weren't trying to award 500 points it would all make a bit more sense to use DND cards. DND cards have never meant that properties should not put the "housekeeping service" card under the door, the same card that typically has ticks for "deliver package, laundry" etc. Reducing HK hours is another issue. I often leave a DND until 3PM if I had a late arrival and will call to ask for service, but in some properties they are already clocking off.
So if Hilton had a consistent policy it would all make more sense.
By the second day, the OP would have received two cards, then a courtesy call from the Manager to ask if all is OK and policy is just to make sure he is alright. Policy does not call for the Manager to enter the room and inspect it. If someone feels so wrong when the guest answers the door, then the property should be calling the police. In this climate, I am sure 99.9% of guests are completely understanding. And in smaller properties, who know and see their guests, I sincerely doubt this is even an issue.
Properties prioritising saving a few measly dollars on housekeeping costs remove a big part of the eyes and ears of the hotel. Incentivising guests to the sum of $2.50 for points to decline service increases the incidence of this. Housekeeping would surely spot suspicious articles in a room and something that doesn't look right. But management decided it's better to save a few dollars on HK. And still, corporate policy only calls for the hotel to check if the guest answers the door, not to barge inside if the guest answers.
And for the thread title, it's a second-day wellness check, not daily, the manager should make that clear.