I think it could be argued that Jellico was partly using the "danger" factor as an excuse.
Contrast the following dialogue:
PICARD: It may be dangerous to take the ship in.
O'BRIEN: Take the ship in where, sir?
PICARD: Into the anomaly, Chief. Lay in a course for the exact centre and transfer all available power to the shields.
TASHA: Sir? Can you give us some explanation?
PICARD: No, Lieutenant, I cannot.
TASHA: Captain, so far we've obeyed every order, no matter how far fetched it might have seemed. But if we're to risk the safety of the ship and crew I think we have to ask you for an explanation.
PICARD: I understand your concerns, Lieutenant, and I know if I were in your position I would be doing the same thing. Looking for answers. But you're not going to find any because I don't have any to give you. I know it is difficult for you to understand, but we have to take the ship into the very centre of the phenomenon and create a static warp shell. Now, this will put the ship at risk. Quite frankly, we may not survive. But I want you to believe that I am doing this for a greater purpose, and that what is at stake here is more than any of you can possibly imagine. I know you have your doubts about me, about each other, about the ship. All I can say is that although we have only been together for a short time, I know that you are the finest crew in the fleet and I would trust each of you with my life. So, I am asking you for a leap of faith, and to trust me.
TROI: I'd be happy to. But first, I'd like to talk about how the change in command is affecting the crew.
JELLICO: I've noticed some resistance.
TROI: I wouldn't call it resistance. More like uncertainty. Most of them had served under Captain Picard for several years. They knew him, they knew what he expected. Now they're being asked to adjust to a new captain and a new way of doing things, and they're uncertain how to react.
JELLICO: I see your point. This all could be very unsettling to them.
TROI: And to you. Perhaps everyone just needs some time. Time for you to get to know and trust the crew, and time for them to understand how you want things done.
JELLICO: I'm glad you brought this to my attention, Deanna. Unfortunately, I don't have time for a honeymoon with the crew. You've clearly given this a lot of thought, so I'd like you to take charge of the morale situation. Please see to it that they make the adjustment to the new routine quickly and easily. I have a meeting with the new Security Chief in five minutes, so the duty roster will have to wait. Thank you, Counsellor. By the way. I prefer a certain formality on the Bridge. I'd appreciate it if you wore standard uniform when you're on duty.
TROI: Of course, sir.
Picard has only moments to avoid the destruction of humanity, but takes the time to get the (bridge) crew on board, Jellico has at least a day before any real prospect of danger but claims he "doesn't have time", this suggests to me that he may be well suited to a role at Starfleet Tactical (he and Shelby would either get on very well or kill each other) or Intelligence, but he's a poor leader in extremis (ie when good leadership is most needed) so an inferior starship commander.