One aspect that needs to be factored in, is that hobbits were not men (or, at least, they were a very distinctive race of men) — in particular they were much less status-seeking than men, and less aggressive. A different species naturally has a different form of government.

Overall, I think that Tolkien advocated a religious monarchy, somewhat on the Byzantine model — Gondor under the Kings (before the Stewards) was the nearest thing in the Third Age (although the religion was vestigial) but this pretty much described Numenor.

In other words, it was a monarchy that united spiritual and secular leadership — in which God chose the King, and the King represented God to his people.

Divine sanction was revealed in The Lord of the Rings by Aragorn’s “miracles” of healing — and healing of a type only he could achieve (curing the Black Breath of the Nazgul King).

The authority of the King was absolute, except that he must not go against the will of God (implicitly) — it just happened to be the King Aragorn’s will (for the good of his subjects) that he left The Shire to govern itself (subject to protection from the King’s Men).

A good, kind King would have regarded Hobbits rather as we regard children or mentally-incompetent persons — creating for them a protected environment where they can conduct their own games safely.

Hobbits could not, and probably should not, be integrated into the world of Men — there could only be some kind of parallel Hobbit society — else they would have been enslaved by bad men.

(I would guess that the Rangers had for centuries been preventing this from happening in Bree, while they were also protecting the Shire Hobbits from invasion).