Add to the mix that Jellico had been brought in both negotiate and prep for a potential war. After awhile though, Jellico treated the war as unavoidable. Which Riker brought attention to and that talks at this point were only lip service. All while Picard’s life hanged in the balance.I think if the episode were any longer that's exactly what we would see...
At that point Riker's out of the mix but Geordi is still there dealing with Jellico not listening to his objections, Troi is there trying to smooth things over and getting brushed off, the crew is still there most likely still unsure of him, the department heads probably think his judgment sucks for screwing up the rosters. If word spread around the ship Riker was relieved for arguing to save Picard they would lose even more confidence in Jellico. If the plan didn't work and war started he would be in deep shit.
Here's the thing, why didn't he just tell Riker something like "we need to get an advantage on the cardassians and we'll try to make a play for Picard, it's a long shot but our only option." Instead, his approach is like "your captain is dead. give up on him. I'm the captain shut up about it or I'll replace you." He had pretty much declared Picard dead before the mission even began. That is a bad move on his part
Picard was already a casualty to Jellico.