The one other point I see is that as the number of recipients
then a priori it becomes less likely that so many people would all
collude to forge a message from Alice. So although you have security
in principle, the deniability becomes a little more questionable in
practice when the number of recipients is large.
Of course this is so - like if you tell several people a "secret" and
want do dement it was you who straied this rumor...