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.