Jacob Levy argues that one of the costs of dual citizenship is that it may give too much electoral power to overseas voters. This is only a serious problem if all non-resident citizens have voting rights, and that isn’t a universal feature of modern democracies. In Australia, if I’ve read the rules correctly, the only non-residents allowed to vote are those out of the country for under 6 years. (And the only non-residents who can enrol are those who have been away for less than 2 years and are away for work-related reasons.) I don’t know what the rules are for other countries (those rules aren’t quite as relevant to me, so I’ve never had need to learn them) but if they are at all similar Jacob’s quite reasonable concern is already being addressed.
UPDATE: Don’t get electoral law advice from me! As Alan from Southerly Bluster notes in the comments, an overseas Australian can keep voting after being out of the country for 6 years provided s/he keeps enrolling every year. And it looks like the law will be amended soon in order to remove even that constraint. Part of my initial point still remains. We can in principle allow dual citizenship without having the worry Jacob alludes to by having residency restrictions on voting. If that was the only reason for not wanting dual citizenship, there is a workaround. But the (only!) data point I drew on in arguing that was mistaken. Much thanks to Alan for pointing me to the relevant bit of the law here.