At the(small) hotel chain i work for:
We do not accept reservations inquiries on the day and say it's fully booked
Unless we have more than 20 rooms left.

Another reason is that our chain also sells the rooms on online platforms like booking.com etc.
Capacity on those platforms has to be announced in advance (depends on the chosen contract and commissions).
So sometime we do have rooms left, but blocked on those platforms (and we are not allowed to redirect them to those)

Go figure...