Issue with Boarding on Turkish Airlines Flight from Istanbul to Trabzon

I wanted to check in my luggage for a THY flight from Istanbul to Trabzon with 30 minutes left before departure. They refused to let me board, claiming the plane was closed. I didn't carry my hand luggage because I have a 98% health disability and couldn't carry it. I put everything in my suitcase, which was 6 kg over the limit, and they charged me 90₺. Despite my explanations, they didn't accept it and insisted I pay. I just wanted to board the plane.
In the end, they let me board after making me wait at the gate. Other passengers were still in line. How can the plane be closed? They said they would let me on if there was space after the passengers boarded. I had bought my ticket two months ago but hadn't selected a seat. After my insistence, they finally let me board.
I realized that they wanted to sell my seat at a higher price to someone else. There were three other people like me. Two women and I managed to board after pleading. This was the first time I faced such an issue. I never select my seat. Another woman had arrived at the airport two hours earlier, checked in her luggage, but was not given a seat number. She also faced the same issue. How can they claim the plane is closed and refuse to take luggage when passengers are still waiting at the final gate? This commercial approach of causing inconvenience to people is inhumane.