So the first thing to note is that of course, the ALL late check out is not a "always" but a "subject to availability" benefit. That's different to, say, the FHR late check out benefit which is "guaranteed".

Some hotels have a bad tendency to say no to (complimentary) late check out as a matter of course even when they could easily do it - Sofitel New York will come to many people's minds. But then in fairness, I think that is common to many NYC hotels in general and I have had exactly the same issue with, say, Hilton properties (also as a Diamond).

Where hotels are not openly antagonistic, though, I would say that in my experience, unless the hotel occupancy is particularly low, it is actually the norm that the late check out (or at least the exact time of the late check out) has to be confirmed in the morning of departure and not before. The reason for it is that this is the time when the hotel has the best understanding of occupancy and room allocation. In that sense, the three crucial questions are: 1) is the hotel quite lightly or quite heavily booked on the day of your departure, 2) has your specific room been allocated to a new guest on that day and 3) if so, does the hotel have an ETA for the new guest.

The point is that of course, a hotel can't give you a 4pm late check out if they have another guest checking in the room at 4pm. That's just not possible and that wouldn't be fair. On the other hand, if your room is not to be reallocated on your day or departure, or if you want a 2pm late check out and they know that the next guest won't arrive before 10pm (and this is a luxurious enough hotel that they have continuous availability of cleaning staff - note that many cheaper properties only have cleaning staff at very specific times to save money which further complicates things), then they should make an effort.

Personally, I certainly wouldn't do the "manager" thing. Everyone to their own but this is simply not my style unless there is a significant problem, and being told something subject to availability is not available doesn't qualify by my book. However, I would feel free to ask specific questions such as:

1) At what time will you know for sure whether I can keep the room?
2) If you can't confirm 3pm now, could you at least confirm - e.g. 1pm and I'll just check if more is possible in the morning>?
3) (If booking several rooms) I understand you may be heavily booked, but would it be possible to assure that we keep at least one of the rooms please?
4) Do you know if there is a new guest allocated this room today?

I personally find those approaches (polite and to the point) typically more productive. The only case where I'd be getting really annoyed is if I'm told I can't get a complimentary late check out but I can get one if I pay.