Coins are fungible and PM coins are, if sold in bags are considered almost equivalent to bullion. The dealer may buy the silver coins and simply sell them rather than smelt them. I can't see where it's an advantage to a refiner to purchase a $15,000 bag of coins only to melt them down into $15,000 worth of silver bars. It's what makes money for the refiner, not the process. Silver junk, including silverware and all sorts of silver containing jewelery don't have this advantage and thus this is why they are worth less to a refiner. They have to be refined before they become a sellable asset.
You have to think outside the box. Just as there are coin dealers that don't melt coins, there are jewelry & silverware dealers that don't melt either.
Rule of thumb is, if it's not marked Sterling or has a .925 mark it's almost, for certain, silverplated. Also, anything marked EPNS isn't even silver plated. Its Nickle Silver and also called German Silver. Usually an alloy of 60% Copper, 20% Nickel and 20% Zinc. Quadruple plate means the piece has more silver plate thickness than most other plated items. Some refiners do refine silverplate. The refiner I spoke with, wouldn't even consider doing it unless I had 500 kg or 1,110 lbs. I understand the recovery rate is 4.66% of the original weight of the silverplate or less depending on the quality of the silverplate. After paying the cost to refine and the gas money to get it there, I would likely end up losing money.
Even though dealers cite high smelting cost in order to purchase at deep discounts, sterling silverware and jewelry are most often sold at premiums over melt, rather than actually smelted.