A huge difference between then and now is the amount of media and other distractions that now come with the captaincy.
We have no idea if Itoje can cope with that and a Lions tour visiting the world champions wouldn't be a great time to find out that he couldn't. I'm inclined towards the view that if he really was that much of a natural leader he'd have been given a bigger role with Eng esp given the paucity of other contenders.
AWJ is used to that level of scrutiny and wouldn't be fazed by it. He's got enough Lions experience to know what it takes to keep everyone honest off the pitch and on it you'd prob still get honest 7/10 performances from him. Itoje occasionally delivers 9.5/10 that turns matches, why take the risk of fettering one of your potential match winners with a pressure that you have absolutely no idea if he can handle.
There's a good argument that the Eng captaincy should move from Farrell. If that happens soon, Itoje gets it and is successful then I may think differently. But right now, while not ideal, AWJ might just be the least worst compromise candidate.