Those who bet that there won't be a nuclear war next year will expect to win some money and if that money is half of a basis point they are not going to bother.

Half a basis point is half a basis point. Bond traders would prostitute their grandmothers for a regular half a basis point boost to their returns.

Who will be the source of money that pays the winners?

The source is everyone who takes the other side of the contract? PMs are two-sided.

And if this particular market will be subsidized, well, then it becomes free money and your prediction ability goes out of the window.

I don't pretend to understand how the LMSR and other market-makers really work, but I think that you can't simply trade at random to extract money from them.

Especially bets with moral overtones ("You bet on a global pandemic happening? What are you, a monster??")

Seems to have worked so far with the IARPA bets. (Admittedly, my own trades on ISIS being overblown didn't work out too well but I think I did gain on the various flu contracts.)