I don't think that saying "oh, by the way, someone get that fucking fish out of here" is making it the number one priority. He was the man for the job and he got the job done. I don't see any problem with him turning Captain Stubing's Love Boat into a proper military vessel for a few weeks.
It was literally one of his first orders, (after changing the duty roster so there would be less personnel at a time to carry out any of his seemingly arbitrary/petty orders) and he made it even more forcefully than most of the other orders he gave at the time. It was clearly a priority for him.
If the Cardassians were going to be spending even a moment inside of the Captain's ready room (and spoiler, they didn't, that would just be retarded) then I could understand it being a priority. As it was, it just came off as Captain "I'm the alpha wolf" Jellico, pissing on the ship to mark his territory, even after he had already spread personnel unnecessarily thin to carry out his orders at that point.
In fact, maybe with the fish that's what he was trying to show a crew that, let's face it, could be a little soft. If you ever watch "Bar Rescue" John Taffer likes to do a "show firing" in front of everyone to let them know they're not in Kansas anymore. Lots of NFL coaches who are trying to turn programs around often have to tangibly let the team know things are different going forward. Jellico telling Riker to grow up and setting up his office the way he wants in the name of military discipline isn't being unduly hard. It's showing them they need to nut up if they want to survive.
If that was actually his intention (and for the record, there is no reason to believe it was) Then he's an even shittier leader than I gave him credit for being. That is not the mark of a good leader. It's already explicitly shown that Jellico is a micro-manager to the extreme.
As far as leadership styles go, that one rarely works to inspire loyalty or morale among your underlings, especially when the things you are micro-managing are just petty bullshit to show your new crew that you're the "alpha wolf" (Jellico's own words more or less, just not about himself.)
It's also particularly telling that Jellico didn't even bother telling his underlings what his strategy was when meeting with the Cardies, (i.e. making Gul Lemec wait for him, just to show who the 'alpha wolf' was.) That apparently wasn't a bad strategy... but why the fuck didn't he tell the crew about it until Deanna came to ask him why he was sitting on his ass doing nothing? All the more damning, given how hands on was for literally everything else. What if Deanna hadn't come in to ask Jellico what the fuck he was doing? His plan seemed dependent on that... So he's literally counting on his crew questioning his (as far as they know) stupid orders? That's a shitty Captain.
You know, I don't even think Jellico is even remotely this bad, but from what I just said, he does remind me of another shitty leader from a more modern sci-fi property...
They are an exploration ship, but they still are part of the Federation (which is basically the military) and they need to follow protocol and obey orders when the situation requires it. I can't remember the episode that much, but the situation with the Cardassians was tense, so they all need to put down the bs and act accordingly. If a current science vessel is ever found close to any enemy territory, they can't say "wait, our captain is not very strict during peace time, we need time to adapt to a new situation". That's what Riker and Troi were asking and Jellico was perfectly right telling them to stfu.
Nobody's saying that they shouldn't follow orders, but calling the Federation "basically the military" is almost as ridiculous as the people who insist that Gene's apparent vision that "no they aren't the military all, similarities be damned".
There is obviously some overlap, but Starfleet's primary mission is clearly one of exploration. I've said it before, and I'll say it again, they're mostly a bunch of fucking science nerds.
I get that isn't quite so cut and dry. Jellico himself is clearly a military man (presumably by necessity) but I don't remember any other main character in Trek being explicitly stated to have fought in the Cardie war besides O'Brien.
I'm guessing that Jellico was at least a decent war time captain against the Cardies, he clearly understood their general psychology well enough, but I wouldn't have put him in charge of the ship negotiating with the cardies during supposed *peace time*. He could have just as easily been brought in as a special consultant to the captain. (And I'll be right back to that in a second.)
I get that the writers wanted conflict between Jellico and Riker, but they did a poor job with it. Riker's real reason to be mad was that Jellico wasn't Picard. No wonder he doesn't want to leave the Enterprise, he knows his future crew could have an asshole treating him in the same way he treated Jellico.
I do agree that Riker kind of acted like a bitch during that exchange at the end where he basically asks Jellico to beg him to pilot that mission to mine the Cardie ships, that wasn't professional at all.
But you're wrong. Riker's *real* reason for being mad, and this is obvious even if it was never explicitly stated in the episode, was that Admiral Bitchaev (and I'm never going to stop calling her that, because it fits her so well.) put the micro-managing shitty leader, in command of the Enterprise instead of Riker himself.
Mind you, this was mid season 6 TNG. Riker had already more than proven himself capable of being a Captain- He was literally the hero of Wolf 359 and he should have been promoted for this mission. If you absolutely needed a Cardie expert (and I agree, Jellico fits.) then Bitchaev could have just had Jellico be the cardie consultant to acting Captain Riker.
This might have just been me reading to closely into it but I always thought the purpose of Jellico and his actions was to get the Enterprise ready for war should it be necessary as Picard and co were running a risky operation and the Enterprise would be one of the first ships to respond given it's proximity and the fact it is the Federation flagship. Jellico's uprooting of the command structure was to get the crew prepared so that they wouldn't be flailing should war be declared.
He still did a really shitty job of it. I've already said, most of his orders were arbitrary bullshit. Even in the (2 part) episode itself, none of his orders made any difference. Overall, he was just different to mix it up... But at the end of the day, there were 4 lights, so nothing ended up changing. Even the fucking fish came back to the ready room by the end of it.