Can I ask why it's such a big deal to hide influence?
heh... when I first read this I thought you were asking SP why it wasn't working already. :3 In case the other folks are correct, and you are in fact asking why someone might want to hide how much moniez they have from strangers, here is my take....
What it comes down to for me is the answer to "What is the purpose of CIT for me?" or, I guess you could say, "Why would I want to go through the trouble of using CIT?"
On the one hand, it is a way to share information about my characters with other people. For that purpose, organizing the information that is otherwise available in game is desirable: level, powersets, bio, picture, server, and so on. It is nice to have options for displaying that information in various ways that might be helpful in sharing or coordinating with other people, like a URL I could share with them that would only show my characters from one server, or sort the list in a particular way, etc.
Another use is as a reference that helps me keep track of my characters. In that regard it is useful to have another view that collects and displays, to me, all the limited extra info the game exposes to your client software. I may decide to make some or all of that info generally-available to others, but the default should be to hide it since, by default, people cannot see it ingame.
Merging those two purposes also creates some additional interface needs. There are characters that I want to keep track of, but that I am not looking to share. I may have made them for future use, or I may have made them for some specific themed team, or maybe ED messed up their playstyle and I am just not ready to play them again yet. Regardless, that is where the hidden character feature comes in.
So, CIT needs to have two views to cover those purposes: what I see, which is everything, and what everyone else sees, which is the information I want to share (and that should give no hint of the existence of whatever it is I have chosen not to share).
I can think of a third purpose, which I guess could be described as displaying accomplishments... how many alts you have, say, or how many 50s, or how many badges a character has, whatever. That isn't a particular interest of mine, but I don't see any reason that there shouldn't be display options to facilitate that, too.
Serious bonus points if there are more tiers of access control than just "me" and "everyone else". CIT friends should be an access category, at least. But, like I said, that is "bonus points" territory... I can live without that and still use CIT for the basic purposes I listed.