That term conveys a number of advantages for the writers: 

1. Coucils are generally democratic (or at least republican), and thus generally **viewed more favorably by modern audiences** than kings, emperors, etc.  A powerful group governed by a "council" gives the impression of at least a semi-enlightened society.

2. At the same time, the term "High Council" retains a more formal, even ceremonial feel than many modern terms, and that **adds gravitas to the story**.  He's not just a Congressman, he's a "Member of the High Council."

3. It's also a **suitably generic term** that allows the writer to establish certain facts (e.g. it's made up of multiple people, decisions are made by vote, etc) without getting bogged down in minutiae (e.g. is it a congressional or parliamentary system?).  It's just a Council.

4. In many cases, it offers **an opportunity for palace intruige**.  A Council is made up of individuals, and those individuals can disagree, betray, persuade, or replace each other.  A enemy monarch must be opposed directly, but an enemy on a Council allows for the possibility of allies with similar power.  "If we can just convince Senator Whosawhatsit, we can stop Consul Evilface by finding and dismantling the Apocalyptathing!  Only a member of the High Council has that kind of power!"