Bits and pieces suggest to me that Konami originally had plans to incorporate Joseph as a playable character in some form. The idea may have been scrapped for resource reasons. The year 2004 wasn't a particularly great time for KCET as Konami was planning to move their gaming division to the US.
The idea of dual playable characters was recently mentioned in a Silent Hill 2 Remake interview with Okamoto, Ito, and Yamaoka [1]. According to Ito, when the team was brainstorming Silent Hill 2 at the time, they apparently had an idea to have the protagonist switch out with another character midway ala "Lost Highway." The idea was scrapped as they thought it would be too confusing for the players. Silent Hill 4 was designed to be experimental, so it would make sense if they wanted to revisit that idea with Henry and Joseph.
The "Another Red Diary" entries, which I translated long ago, describes Joseph finding, presumably, the Crimson Tome on the second floor of Wish House. However, when you try to visit that room as Henry, he will mention that the lock is broken and that he cannot get in. It's a rather pointless trek for Henry to go up a flight of stairs just to find a broken lock.
I think the problem with Joseph being the sole protagonist is that he's destined to be doomed. Players generally don't like having worked so hard just to get a canonical Bad ending. But Joseph and Henry traversing the same location, but only separated by time could make for some interesting gameplay and story.
[1]
https://www.ign.com/articles/silent-hil ... -interview