Around 2017-2018 I remember reading a really interesting article about how the Obama White House handled letters to the president. The vast majority of letters (hundreds per day, IIRC) were answered by staffers, but each day they would select 10 letters that Obama would read himself. He didn't personally write out a reply, but he'd make notes for the staff about how he wanted to respond. No idea how Reagan's team handled it, but it's at least possible that he was personally involved in the reply.
Reagan's administration worked in the same way. But Reagan himself was a prolific correspondent, and personally dictated a much greater share of those replies than most 20th century presidents.
(Reagan also was known for reading articles and scribbling notes to staff about a note to send "from him" about the content-- quite a few journalists and essayists received Reagan letters).
Would like to see responses from the Alzheimer's years. He got pretty bad towards the end. Biden sounds like a 20 year old in comparison. Trump is still off in cofeve land.
