An interesting topic.
Given that an obvious original growth area in New Arnor would be
around Annuminas and Lake Evendim, and that Bree would clearly
grow and prosper, and that there would eventually be a rush to get
primo seashore properties (already somewhat developed) when Cirdan's
lads left the Grey Havens

, The Shire couldn't be economically and
politically isolated forever. For one, an economic/political alliance of the Shire and Bree would be potent.
P.S. Oh, and who would be Aragorn's governor in New Arnor and what would be his powers. In a generation or two a situation could easily arise akin to
Charlemagne's descendants.
P.P.S. Since hobbits are somewhat distant relations of Men, what about
mixed marriages of hobbits and "short people" (who certainly have the right
to live

). Perhaps hobbits evolved back into Men, aside from the remnant
JRRT tells of in modern times. Hmm?
P.P.P.S. Some of the above is rumored to be not totally serious.