Even if just for admins and mods, A gallery would be helpful !
Getting users to use a Gallery is much harder, as you say.
Having a Xenforo Gallery that works in conjunction with Flickr, Photobucket and Screenshot.com is a good idea.
Members would really like that.
I would like to be able to insert gallery images into posts
	
	
	
		Code:
	
	
		[galleria]company.logo.png[/galleria]
	 
 Photopost probably won't do that easily.
Part of the reason why vBulletin Galleries didn't take off was .... they weren't integrated into the forums.
If somone posted a screenshot and it showed up in "New Posts" that would help drive the Gallery.  I dont know if any Gallery did that.

The images won't be a thread, the link would direct people to the gallery and be able to comment on the image. (comments = replies).
Maybe members couldn't even "Announce" a new Flickr image via a link showing up in New Posts.
Getting forum members to post images might be best done by 
bundling some screen grabbing software.
You could click a button,  [click]

take the screenshot [outline screenshot with dragging]
and it is automatically uploaded.
(Probably hard to do ?)(Are there some Firefox / Chrome tweaks that could grab images from the browser ?)
Other ideas:  make it easy for at least keen members to upload images from their cell phone [Take Picture] select ... "Post to forum".  Might work on some sites.
Things I think:
(1) Galleries are important.  Admins and Mods will use them the most.
(2) It is hard to get users to participate in the gallery.   Lots of things could encourage participation.