it's not the source, it's the luck of the draw. One supplier does not have anymore silver than any other. It's what's in the local (or regional - that's my own term, not official) coin supply.
Halves don't circulate very widely in commerce. Most of the 'churn' of half circulation is through CRH, with the occasional influx of silver when someone cashes in / spends Grandpa's coin collection. That can happen through many avenues: unsuspecting widow(er), heirs, or some crackhead who broke in somewhere and stole it. Those are not nearly all of the sources, but I'm sure you get the gist of it.
Either your local supplier (Brinks, Loomis, Guarda, etc) has silver that day, or they don't. Everyone on here who has searched more than a month or so can verify that some days you'll get a few in a box, most days you'll get skunked (we're not talkin' CnC here, BTW

), and very rarely, you'll hit a big score.
It's like fishing. Some days you won't get a bite, others, the fish are jumping into the boat.
YMMV