It’s an ethos thing. Obsession isn’t a bad way to describe it!
The Lost City project exists to preserve history. The short logout timer is historically significant, and it is the way it is partially to balance other historically significant mechanics (dangerous random events, brutal death).
There’s something to be said for the effect the timer has on gameplay in general as well. Nearly everybody you see logged into the game is fully present while they are playing. Without as many opportunities for afkscape, there is a more cohesive sense of community. This part is pretty subjective but I think it’s nice.
I don’t deny that certain gameplay styles are more difficult or impossible in 2004, but it’s a historically important opportunity for players to realize those types of gameplay were rare or nonexistent at this stage in the timeline. That stuff was created much later on, by OSRS content polls and third-party+mobile clients.
The logout timer will be changed when the game progresses to January 2009, when Jagex finally changed it to five minutes on RS2.
This is valid! Note that you are able to opt-in to 2FA for your account (definitely inauthentic for the era – practicality occasionally wins over ethos 
). This way you can set an easy-to-type password while keeping your account secure!
Hope this helps, have fun out there.