Interesting working assumption but it is not based on anything mentioned in the episode. Just take a look at how Picard (or if you wish to in addition to that Kirk as well as any other Starfleet captain we have seen hitherto) has run the flagship and how he has dealt with admirals, he has a lot of autonomy.Captains aren't autonomous. Sometimes they have no choice as to how they proceed. Nechayev points out that the Enterprise is chosen solely for namesake value, because it's an historic ship that's name carries weight throughout the galaxy. Jellico was ordered to take command & conduct a negotiation that everyone predicted would end in a lengthy war erupting
Therefore Jellico had to take a capable ship & crew, & REoutfit them such that they would no longer be geared to their existing mission of standard negotiations & exploration, but rather as a full-time tactical vessel at the forefront of a longstanding fleet war.
Jellico was in a position of having to make necessary changes to that end, before he even beamed aboard. Whether the changes were his call or a joint understanding with HQ is unknown, but one thing is certain, if the standard "Smooth" operations of the ship were enough, then they could have just put Riker in command & brought Jellico in as a negotiator
There would have been no one better than Riker to keep the ship & crew at their peak standards, but clearly that was not what HQ wanted, which is why they handed the whole ship & mission over to Jellico. It's evident that everything Jellico did was to give Starfleet what they wanted, & not to merely to be a douchebag. Why would anyone chosen to prevent a war, or begin the initial stages of one ever behave in such a manner?
No, the problem was that Jellico was in a hard spot where he had to do something that if it were Picard doing it with the ENT crew, then no one would ever give a second thought. They'd just bust ass, & do everything he asked, because they have implicit trust in him, from years of service together, & though I figure Jellico has that trust on the Cairo, he had no such luxury on the Enterprise, nor did he have any time to build it. As such, he just had to push for it, knowing they could deliver, whether they liked him or not, & expecting that they wouldn't.
Even in a dire situation like the one from "Chain of Command" Starfleet Command certainly will not tell the captain of the flagship to run four instead of three shifts or in general micromanage the ship from a distance.
Furthermore I also don't buy the assumption that the Enterprise is totally converted into a tactical vessel, there have been many dire situations near or in the Romulan Zone that did not make a warship out of the Enterprise. There is a reason Starfleet's largest ships are multi-functional, that exploratory and military tasks are not separated.