The Idea that Kirk was a commander when we first saw him makes perfect sense, but it is kinda hard to accept that Pike would have been a lieutenant in command of one of the most powerful vessels in the fleet. I wonder what they were thinking when they designed the rank system for the first two episodes?
As an analogy, Colonel and Brevet Major General Nelson A. Miles was on the trail of a group of hostile Sioux in 1877 when the trail split. Miles divided his command and led the group that followed the smaller trail while putting Lieutenant Baldwin, who had more experience fighting Indians, in command of the larger force that followed the larger hostile trail. An army lieutenant is the equivalent of a lieutenant junior grade in the navy. Special circumstances can put an officer in a more important command than is usual for his rank.
Is it absolutely certain that Pike was in command of the same
Enterprise as Kirk commanded in TOS episodes? It did have about half the crew size. Perhaps it was a smaller and less important class of ship that only looked like a constitution class ship on the outside because all starships had the same general appearance.
Possibly the Federation has hundreds of starships of various classes that all look like Constitution class on the outside, assigned to Starfleet, Starfleet Reserves, UESPA, Vulcan High Command, planetary defense forces, etc. etc., and possibly only 12 or 13 are like Kirk's
Enterprise in being Constitution class starships assigned to five year missions to seek out new life and new civilizations. Thus Pike's
Enterprise might not have been one of the most powerful in the fleet.
And, given that UESPA and Starfleet are related agencies that work together, there is some evidence in "The Cage" that the
Enterprise and its crew are more directly in the service of UESPA and Earth and more indirectly in the service of Starfleet and the Federation, while in TOS the
Enterprise and its crew have been transferred and are more directly in the service of Starfleet and the Federation and more indirectly in the service of UESPA and Earth.
Remember that to someone as old (however old that was) as Commodore Mendez Pike and Kirk seemed to be the same age. But Pike was the "captain" (in the sense of skipper and commanding officer) of
Enterprise thirteen years before "Menagerie", and Kirk was only a captain for a few months or years before "Menagerie". And Kirk was also supposed to be the youngest starship captain in Starfleet so far.
One way to get around this paradox is to suppose that Pike was a few years older than Kirk and was a lieutenant in UESPA and/or Starfleet when he became the commanding officer of the
Enterprise sometime before "The Cage" and was promoted to lieutenant commander, commander, and finally captain, and was at least a little bit older than Kirk when he was commissioned a captain.
Another possibility is that Pike had two different ranks of different types at the same time. For example, Pike might have had different ranks in UESPA and in Starfleet, just as, during the US Civil War, many officers had different ranks simultaneously in the United States Army (USA) and in the United States Volunteers (USV). So possibly regulations allowed Pike to command in his higher rank but made him wear the insignia of his lower rank.
We note that in "Hero Worship" when LaForge was a lieutenant commander and chief engineer, Data, who doesn't make mistakes, called him "Lieutenant LaForge". Thus LaForge seems to have been both a lieutenant and a lieutenant commander simultaneously and it must have been proper to refer to him by either rank.
Another difference in ranks during the 19th century was between substantive ranks, that officers were, for example, paid in, and brevet ranks that were sort of honorary. After 1869 regulations allowed officers to wear the uniforms and insignia of their brevet ranks when off duty and to be addressed by their brevet ranks. Thus on June 25, 1876, Lieutenant Colonel and Brevet Major General G. A. Custer is quoted as addressing Captain Benteen by his highest brevet rank as "Colonel Benteen".
In the move
Fort Apache Lieutenant Colonel Thursday arrives at Fort Apache wearing the frock coat of a major general and Captain York calls him "General Thursday". Thursday says his rank is the rank he is paid in, lieutenant colonel, and York explains that the remembers Thursday from the war as a general. But if York doesn't arrest Thursday for impersonating a general he would be violating army protocol if he doesn't call Thursday "General Thursday". A lieutenant colonel didn't have the right to wear a major general's coat unless he was a brevet major general, and if he was a brevet major general he had the right to be addressed as general. So that scene is very weird.
As I said, army officers had the right to wear the uniforms and insignia of their brevet ranks while off duty after 1869, and even when on duty before 1869.
So possibly in TOS where some officers are called lieutenant commanders and wear the insignia of full commanders, they might have two different ranks of different types. Regulations might require that they be referred to by their lower ranks of lieutenant commander but allow them to wear the insignia of their higher ranks of commander.
And perhaps Pike also ears the insignia of his lower rank but commands the
Enterprise in his higher rank in "The Cage".