I'm intrigued but unconvinced. If a creature gives you The Monarch, you keep it if they deal with the creature but you also risk giving it to the opponent if they have creatures (i.e. mentor/delver/anything in Vintage).
The ability to become monarch is also back breakingly powerful to decks that do not win on the ground.
An extra card each turn that cannot be interacted with except by creature combat is pretty spicy, but it seems like a slightly different version of what Library of Alexandria already does. The restrictions are different, but the result is the same. I can certainly imagine games where this is indeed back breaking.
However... we have yet to see any cards that make you the monarch for cheap. Marchesa does a pretty fair impression of that Rakdos Witch legend who saw play for a few minutes as anti-Jace tech, but it's not clear she's playable today.
Let's say they slap this on a Bob-like creature.
Bob the Builder
When this enters the battlefield, you become the Monarch. Lose life like Bob when you draw a card off of the Monarch ability.
On the one hand, they can't stop you from drawing if they have a bolt. On the other hand, you're vulnerable to Notion Thief, and more importantly, Creatures Not Named Notion Thief. Getting your crown stolen is pretty bad game.
It ultimately feels like a high-risk, high-reward mechanic, which is good for Vintage. If we see cheap enablers, then I think we start talking seriously.