But the way out would be that the Judge could declare, "I didn't rule there was no Santa Claus, I ruled that Mr. Kringle had failed to prove that he is THE Santa Claus." That was why his political handler had no objection to what happened to Kris, he just wanted to make sure the Judge didn't declare there was no Santa, period.

Earlier Charlie is telling Judge Harper that if he rules that there isn't a Santa Claus then he likely would be defeated for re-election because of disgruntled labor unions as a result of fall off in sales of toys and yet he had no objection to Harper having Kris committed which would have the same result in the childrens' eyes, no toys delivered. By Christmas Eve most of the presents had been bought by parents and I guess they could explain that inasmuch as Kris was unavailable his helpers delivered the presents.

So what really happens to dead letters. Are they sent to the dead letter office to be shredded, burnt, or wait to be claimed?

Yes, I guess he would at that. (I used to work in a post office. It's the dead
letter
office.)

Gailey got lucky. Without the post office trying to dump those Santy Clause letters out of the dead end office he would have lost the case.
Is very bad to steal Jobu's rum. Is very bad.