Darcy has, up until the event of his proposal, never had his behavior assessed by anyone outside his own elite circle of friends and family. The one exception, of course, is Wickham, but Darcy has every reason to discount everything and anything Wickham might say. Elizabeth is the first to become an acquaintance of Darcy who sees the surface presentation of intolerance, superiority, critical judgement, and pride. Elizabeth is the first of Darcy's acquaintances to tell him how he seems to people outside his private group. Darcy is devastated. As he suggests, he always thought that his noble and upright character and actions would universally speak for themselves.
"As a child I was taught what was right, but I was not taught to correct my temper. I was given good principles, but left to follow them in pride and conceit." (Darcy, Vol. III, XVI; Ch. 58)
Elizabeth had to make the accusations against Darcy after his proposal in order to hear his explanations. It was critical for her to hear his explanations in the letter the next day because these gave her new insight into his and her own character. These exposed the realities behind his actions, especially against Jane, which was the critical foundation for her changed opinion about Darcy; without something to force his hand and propel him to explain himself, Elizabeth would have had not basis for a changed opinion. Equally critically, Darcy's explanations exposed her own folly, prejudice and pride to her comprehension.
"I, who have prided myself on my discernment! -- I, who have valued myself on my abilities! ... I have courted prepossession and ignorance, and driven reason away, .... Till this moment, I never knew myself." (Elizabeth, Vol. II, XIII; Ch. 36)