You wouldn't, except that it may not be outfitted for a specific mission & it would be more of an issue to refit it (As Jellico does fairly quickly) than to just send someone else, which it wasn'tIt would still seem to be easier to just make the Cairo the new ship of the sector, than to play musical chairs all over the place, especially since they're disbanding the ENT-D's command structure to man their secret mission. Nechayev makes it clear that the name value of "The Enterprise" is why they are sending that ship. It just strikes me that Jellico is put in command of her for that reason, otherwise, the smarter course of action would be to just reassign the 2 ships, because The Cairo would need much less restructuring
The Galaxy class is the Federation's top dog at that point. Why send a lesser ship?
My overall point is that it would be short sighted to think that when they put him in there they had any other notion than that he should run that ship how he runs ships & tackle that mission the way he tackles missions like it. That anyone has objections may be fair, but for anyone to hold a grudge against the man, including Riker, is just wrong. No one has any grounds to say he is doing anything out of line or reckless or counterproductive even. He gets the exact result he needs, as soon as everyone wraps their heads around how to deliver itOf course it is. Jellico is probably more of a known commodity in the captain's chair than Riker is. Especially in regards to the Cardassians. Probably also their best military strategist with Picard sidelined.
The military is usually far more flexible than what we see in Star Trek.
He was the right man for the job, & all Riker does in that episode is show multiple times how he wasn't