I didn't buy a house through an intermediary. Is it reasonable for the real estate agent to let me pay the agency fee?

You shouldn't give money to the agency, because you didn't buy the house once, so you paid the agency fee, so the contract between you ended. I will not buy a house through an intermediary in the future, so it is not directly related.

If you are more professional, you can go to the law firm to find a lawyer to analyze it for you, so that your heart will be more practical.