I don't think democracy and accountability are so recent concepts as you think... but anyway...
In the military? Okay, accountability, sure. But democracy? No military could function effectively as a democracy. In our system here in the United States, we have the military answering to the authority of the civilians who are part of the democratic process, and of course those in the military personnel can participate in that process and vote for their preferred civilian leadership. But democracy within the actual command structure of the military? Hardly.
Let's also not forget that none of our "hero" captains, not even Picard, ever ran their ship as a democracy. In most -- but not all -- cases, they were willing to listen to the opinions of their officers. But the captain made the final decision, and it was executed without question. Riker even said so himself when discussing command responsibilities with Wesley in "Pen Pals."
And let's face it... the orders Jellico was giving were not out of line or even that unusual. Certainly nothing that would give the crew grounds to question his authority. Hell, not like, say, ordering the crew to poison the atmosphere of a planet. And had those exact same orders been given by Picard, do you think Riker and LaForge would have been whining about how difficult the changes were?
No, this wasn't about Jellico being out of line. It was about officers being, as Riker said in BoBW, too comfortable on the Enterprise and not being adaptable to change. Had Jellico stayed in command longer, I'm sure he would have built the rapport with the crew that was necessary for a less confrontational environment. But, as he rightly pointed out, he was put in command and immediately thrown into a crisis situation and he simply didn't have the time.
Unless a commanding officer is mentally incompetent (e.g. Commodore Decker) or ordering something that is blatently illegal (e.g. Admiral Pressman), any Starfleet officer should be prepared to follow their orders regardless of their "command style."