First of all, the Enterprise-D is not really a direct combat vessel
The Galaxy-class was a Starfleet vessel first introduced in the late 2350s. It was one of the largest and most powerful Federation starship classes of its time, with many serving in the Dominion War.
Shelby comes in and acts like a pompous butt. She does try to peg Riker down several notches by saying all he knows is how to play it safe and sits in the shadows of Picard. Honestly, how much of a moron do you have to be to tell someone who is a higher rank than you that stuff? From just stuff that came out of Shelby, you get the picture that Shelby was a tad immature and not ready to become the first officer of the flagship. Sure she's young and ambitious, but she was also full of herself. When Riker became captain and selected Shelby as the new first officer with a rank of commander, he knew he could help her calm down and become a more seasoned person like how he was.
I think the issue is partly that the Enterprise is a ship of exploration and thus the "military" aspects of Star Fleet were somewhat more relaxed than they would be on a military vessel.
Jellico was coming in to prep to do battle. He didn't want to hear whining about working conditions or see Troi's casual outfits on the bridge. He wanted to give orders and see them implemented - not to have a discussion.
That being said, seems like the Federation should have vessels and personnel specifically dedicated to potential military conflicts. While perhaps the exploration crew of the Enterprise has the ability to deal with a military conflict, the experience and training is far weaker than a military ship.
The Enterprise is also not a combat vessel - it's an exploration vessel.