People are aware of the reason they stopped explicitly showing the letter-writing, right?
By not having to repeat the lesson that the characters just learned and by cutting the actually letter altogether, they are saving precious air-time that can be used for another gag or a bit more character development.
I loved Celestia's little speech about the letters at the end of Lesson Zero because it directly fixed the one (admittedly minor) problem I saw with the structure of season one.

If her highest point of the day is receiving letters, She NEEDS a KING
for a boyfriend OR as a father to tell her to stop reading text messages when duties need to be done.
WAIT, how about a brother to tell her her flanks are getting huge because she doesn't do much.
THATS RIGHT, I would watch an ANIMATED sitcom staring Celestia's family.