If rooms are available why are you made to wait till 3 or after before you are permitted to check in.

To give time for the rooms to be cleaned and given fresh towels, sheets, soaps, etc. Sometimes you can ask for an early check in.

Policy but exception at times will permit to check in a bit earier check at front desk with a smile and patience

Probably because people are required to check out by noon, thus porividing 3 hours for service to clean up the room for the next guests. It's a regulation set in place to ensure there is always enough time for the cleaning service to clean the room after the previous vacancy (and to remain fair and consistent, they keep it as 3pm regardless of whether someone was there the night before or not, otherwise people will begin to complain why someone got their room earlier than others).