Here's a different approach:
Is there anything in canon to support or refute the notion that a space vessel's "orbit" of a given planet could be "powered" for one instance and "natural" for the next? In other words, could the Enterprise and other vessels in TOS/TNG/etc be employing different "orbit" techniques depending on the mission and the skipper's discretion?
The orbit in "This Side of Paradise" must be a natural one as there's no mention of it decaying anytime soon. Kirk says he could stay aboard, but not pilot the Enterprise
. Ditto Exeter
's in "Omega Glory". She'd been there for at least six months. "Court Martial" seems to show a powered one, otherwise Finney's sabotage of the engines would be no immediate threat. The choice must be the captain's, dependent on the mission.