If completing GE encounters was this important to a guild, the leadership would make GE mandatory, and would kick members who didn't, which provides the penalty for anyone who would use it. I regularly cast shame on the perennial 12 who never do any GE in my main guild discreetly, no one's name is dropped but they know who they are.
I just don't see the need for anything that's been suggested, including the original proposition.
Well I can see one advantage, to simply put "tracking" the behavior of guild members by the leadership. It'd make it easier for you as a leader, to set a standard. For example, I'm with my guild for more than 3 years. I nearly always do the required GE every week, however now I have a lot of work to do, and I missed it a couple of times recently.
If the leader has an average up in his sleeve, then he would see it that mine is still very high.
So you could set yourself a standard, like if the average falls under a certain threshold, then you need to make steps.
Hell if it made smartly, you could set this threshold in-game with a simple slider/input, and the ones falling below could be indicated for you ie. with a red color.
If we go even further, it could have an automated notification system, when someone falls below, it'd automatically send him the message you've pre-set.
And if we go even deeper
, under a certain point the member could be automatically dispelled if you want to!
Of course these last things are optional, just wanted to show that it can be made even more useful, especially for GE oriented guilds.