There is a boarding time on every ticket. Anyone who has flown more than once knows this is not optional - closing the gate and departing early is at the airline’s discretion.
Once they started boarding and the queue is empty, they will continue with the procedures for the flight, they have an incentive to keep their on-time stats. It’s not like a train where you can simply step in a minute before it leaves.
There is not a boarding time on any airline ticket; you can book a flight for yourself and look at the issued eTicket. Your ticket will only have a departure (and perhaps arrival) time.
Some airlines print a boarding time for their flights onto their boarding passes, or show it in their app. This is often a fake number simply computed by deducting 30 or 40 minutes from your flight's departure time; it's certainly not adhered to very closely or involved in most contract of carriages.
One reason for this is that an airline is usually not involved in issuing all of its boarding passes, and so many boarding passes simply do not have a "boarding time" on them. Air India is perfectly capable of issuing boarding passes for United, but are unlikely to have easy access a "boarding time" from United (since it's not very important).
United makes passenger obligations clear -- arrive 15/30 minutes before a domestic/international departure. Otherwise, it's an IDB.
Right, I meant boarding passes. Since as you said, (estimated) boarding time is usually set to 30-40 minutes before departure, and gates usually close 20m-15m before departure, arriving 15m after the announced "boarding time" is obviously risky. Not sure what's up for debate here.
According to what? To me "boarding time" doesn't mean anything other than the time they plan to begin boarding. Is there actually a policy that passengers must be present by that time?
What the parent quoted seems to be United's actual policy, i.e. that they'll accept any (domestic) passengers who arrive 15+ minutes before departure.
Once they started boarding and the queue is empty, they will continue with the procedures for the flight, they have an incentive to keep their on-time stats. It’s not like a train where you can simply step in a minute before it leaves.