Overall, it sounds like a dm discretionary-thing.
I had a problem with worshiping multiple gods at first, like someone stated, it seems like an open invitation to cheese, But, I don't find that there are a whole lot of advantages of worshiping multiple gods, because I don't think the CD feats are all that (some are, i guess), and you can only use 1 per encounter anyway (normally), but, then again, I never tried to make an optimized character who worshipped multiple gods.
In our campaign, we have our own pathenon being that we feel that the way it is in the settings is too restrictive, flavor wise (were not high on the settings either: Eberron seems too Arcade-like for us, and FR too PG-13- thus, we make, Forgotten Eberron

. As a result, we make it more so, a matter of worshiping domains.
For example, we have a Paladin who is a paladin of change, luck, and winds, and Avandra seems to be the most appropriate for her. And, yet, besides that, Avandra doesn't fit her, at all. Avandra, actually, irritates the player.
The only thing I'm tried to figure out was, why not worship all the domains? To this, I usually expect a player to have a good story as to how and why they worship multiple domains. If they want to sound cheesy to the rest of the group, then so be it, because it's frowned upon, and that sucks a lot of the fun out of the player right there, being that everyone would think the player was being a cheese-ball.
As far as it not being an option on CB, we really don't use it. We like having at least some remnant of the past of pencil and paper, and an old, dirty, eraser-burned character sheet that is stained and falling apart. We like that (but it does suck when we make a mistake on the sheet)