Skyrim is a game where, despite the fact that you are the most important legendary hero in the land, you start out at the bottom of every faction you choose to join. However, you don’t stay there for long; nearly every faction lets you work your way up to become the leader of the faction and then… do nothing.
A grand total of five different factions let you become the leader of the entire faction in Skyrim, including the four main factions (The Companions, The College of Winterhold, The Dark Brotherhood, and the Thieves Guild) and the vampiric Volkihar Clan in the Dawnguard DLC. In fact, the only major factions that don’t put you in charge are the main quest factions, the civil war factions (although you can reach the rank of Legate for the Imperials and Stormblade for the Stormcloaks), the Dawnguard, and the Bard’s College (which is really just a glorified fantasy MFA program in the first place). You end up as the leader of each of these after the death of their current leaders, including three that you kill yourself. They probably wouldn’t have let you join if they knew you were such a jinx.
However, once you become Guild Master (or Arch-Mage or Harbinger or etc.) you realize they must not have done a whole lot. The game gives you a cushy job, and sometimes work to do, but it’s not really any different from what you did when you were a regular member of the faction. In fact, the faction operates just as easily as it did before, even if you abandon them to run around in the woods of Skyrim for months.
It’s worth noting that Bethesda’s other game, Fallout 4, lets you be the leader of a few factions as well: both the Minutemen and the Nuka World Raiders. Both of these put you in a leadership role right away, but they do offer at least some faction management options through the settlement building system. The raiders even let you make delegate jobs to your underlings and lead squads.
Skyrim could have easily added similar leadership elements to factions. As the Guild Master of the Thieves Guild, you could build on the city influence quests, setting up entire Thieves Guild chapters in other cities. As the Arch-Mage of the College of Winterhold, you could work with professors to do independent research, which might even unlock new types of spells. If Bethesda doesn’t want to add stuff like this, which would admittedly be more work on their part, they could just not put you in charge of every guild you join.
After all, it’s currently possible to become the Arch-Mage of a magic college having only cast five spells in your life. Maybe it’s better that they don’t give you that promotion, even if you are the Dragonborn.