There is a thing most of the players don't like about travian - how time-consuming it is. It is one of the main reasons people leave the game. With that in mind I strangle to understand where the desire to put as many responsibilities as possible on one person is coming from.
A king, by the way the game is structured, has certain tasks - mainly expand kingdom's territory. There is no need to force other tasks on a king (no reason to forbid it either of course)
A duke is even more confusing. The original function of this position is to expand the territory and maybe partially shift a burden of treasuries guarding. Why is it connected in any way with leadership? I watched with horror constant rotation of dukes to gain territory. I know a lot of capable people who will never accept the position because of visibility issue. I can rant endlessly.
Leadership is more time consuming than even you imagine, if done effectively. It is also very often a thankless task, and I cannot for the life of me see how anyone could see it as a desirable position to put oneself in. Way back, I was pretty much drafted into leadership and try as I might, I have seldom been allowed to play out a server without finding myself stuck with a leadership position again. Years ago I had plenty of time to devote to Travian, but that is no longer true. I was a fairly decent leader in any leadership position I held. I think the most interesting one was leading an academy wing, and that one kept me doing sitter checks, giving one on one advice, and spending a great deal more time in other accounts than I spent in my own.
But an alliance, and now a kingdom, needs more than one officer. A leader needs others he or she can trust enough to delegate responsibilities to, such as Offense Coordinator or Defense Coordinator. No one person can do it all, but it works best when one person has the final word. I know the descriptions given when registering of the roles of king and governor do not say a king must be a leader, and we have asked that the roles be better defined. However, a king must lead the dukes and governors in his or her kingdom - else, how could it be a kingdom? With three kings per alliance in other servers, it becomes even more important for governors (or dukes) to fill the slots of any other needed officers. Of the three kings, one must take responsibility for leading the alliance (and if there is a meta involved, one king from one of the wings must lead the meta). That is, if it is all to work. Otherwise you just have a bunch of players who happily (or unhappily, if they are someone's target) sim along never really knowing what is going on around them.
Someone once said that team building is an art. I won't go that far, but I will say that a team is not a team if it is not led. Someone at each stage must do the job.
Travian has always required a lot of time of those who play it. It is just the nature of the game. You are correct in that a lot of people delete because it takes more time than they are able to invest in it. Leadership in Travian requires a great deal more time.