Arrived at gate probably about half hour before actual departure. No gate change just late arriving aircraft. Did check luggage. They should have and could have handled it differently.
They could have, but the "should have" is debatable since your connection was very tight, you had bags checked, and it's not clear if you were at the gate a minimum of 30 minutes before departure, which is a common minimum for international flights. If your (delayed) arriving flight left you with 30 or fewer minutes to connect based on the original connection departure time, it's possible your seats were gone before you deplaned from the arriving flight.
From your standpoint, the delayed flight meant you should have had more time to make the connection, while from, e.g., the gate agent's standpoint, he/she was probably doing everything possible to ensure a quick boarding process and minimize the delay. And, again, the difference between being at the gate 31 minutes before and 29 minutes before can be a big one here. That's just the reality in these days of full flights.