The next time you see sky, it'll be filled with eagles.

He was just doing the Numenor equivalent of a gap year before getting back to it tbf..

Yeah, you know how blue bloods get about jewelry..

The Thain is specifically referred to as effectively a monarch in The Fellowship. It's that the Shire both doesn't have any problems and hobbits not really going in for eviiiiillllll in the first place that he doesn't really have much to do. Plus, the Dunedain and nearby elves are doing all the real work to keep the Shire safe so they don't even have a serious militia for him to seize control of and rule with a tiny iron fist.

Peregrine Took inherits the title Thain. Merry Brandybuck is his first cousin, and the Brandybucks hold the title of Master of Buckland, ie are literally a lesser ruling noble family. The Baggins are related and wealthy but don't seem to have any particular authority. The almost certainly did somewhere, Bag End didn't build itself and is apparently quite desirable, with Bilbo being wealthy enough to be leisure class even before his adventures. The Sackville-Baggins, for example, hold the hereditary title of Chief Sheriff and have enough cash on hand to buy Bag End from Frodo with no distress.

Tolkien was a pretty rot-brained monarchist, as a Brit born in the Victorian age. About as good an example as you could hope for, but still absolutely on that divine mandate train.