Elizabeth's rejection of Darcy was all about him. And he does show more grace to Elizabeth at the end, and clearly was thinking about what Elizabeth may be thinking:

"You may possibly wonder why all this was not told you last night; ...
If your abhorrence of me should make my assertions valueless, you cannot be prevented by the same cause from confiding in my cousin; and that there may be the possibility of consulting him, I shall endeavour to find some opportunity of putting this letter in your hands in the course of the morning. I will only add, God bless you. (chpt 35).

The ending is courtesy itself.

Unmarried, unrelated men and women could write to each other on business, for example there is a famous exchange of letters between JA and Mr Clarke (link below), which no one thought meant they were engaged. In the case of Darcy and Elizabeth, it comes across as more of a business letter than a love letter, but neither of them could let on what the topic of the letter was since that would mean letting on to the proposal and to Elizabeth's reply. So keeping the letter hidden is the only way to keep what has passed between them quiet.