I'm surprised at the idea that Riker should have volunteered without being asked. All his previous recommendations to Jellico got him nowhere.
If Picard's life (not to mention preventing a war and his Starfleet oath) were really that important to him, he should've been first in line to volunteer to fly the mission. Making Jellico come to him and ask made Riker look like a selfish dick.
For me, Chain of Command
was the final nail in the coffin for the character.