I can't imagine anyone having a problem with you taking charge of this thing.
As for an opinion on who can participate, if they're not on the current naughty list, let them in. Give them a chance to prove themselves.
There will almost certainly be some drop-outs, but I personally don't have a problem with giving and not receiving a gift.
It would suck, of course, but I ain't slitting my wrists over it. They can just go on the naughty list for next year.