Gondor and Arnor a handfull

[Mandos]

Also, the two kingdoms were very much in touch with each other. The had all seven seeing stones! Gondor had to look after its own survival since it was bordered with Mordor. Just as Arnor had to look after it's own survival even though it was fighting amongst itself while being attacked by the witch king. If there had been a strong high king at the time, both kingdoms would have been made stronger and warded off the decay that wreaked havoc in the time of the Fellowship.And, if it wasnt an empire , what was it? They controlled or had discovered their known world.