No, having sufficient food --that people have paid for, by the way -- wouldn't necessitate them raising the price at all. Those desserts aren't all that high-quality, and don't cost anywhere near what the party costs. There's no excuse for them running out of items halfway through the party and not replenishing them. It's either poor planning or just Disney being cheap.
I work as an inventory manager, and looking at the supply side of inventory is right up my wheelhouse. Disney would love nothing more than to have exactly the right amount of each dessert every night, so that no one complains about running out, and there's no leftovers. Everybody wins! However, predicting that exactly is neigh impossible. They know about how much people want every night from seeing what people wanted previous nights. They have averages, but an average is just that, an average, it's not telling me what the next group will want precisely.
Having sufficient food means that you get dessert. It doesn't mean that you get to have the full spread given to you from start to finish. It's like with hotel reservations. The fine print says that all Disney promises you is a room, they don't even promise you the resort you picked and paid for until you're actually in said room. The dessert parties are the same way. They have never promised that they'll continually have chocolate cake and ice cream and sprinkles. They say that it's offered.
If 20 people at the party suddenly want to load up on the chocolate covered strawberries, what can we do? If 2 tables of 8 all want a 3rd glass of sparkling cider, what can we do? They can also say "sorry, we're out of x, but please feel free to try any of the other desserts." They can't, or won't, spontaneously make more key lime tarts because a table took them all.
There's no way for Disney to know exactly what people want until they get there, and by that point, there's no way to shuffle the supply. Even doubling the inventory still is no guarantee. It's more likely everyone will get what they want, but you'll get that weird night every once in a while where something would still run out. In this case, there's also the increased chance that desserts will get tossed night after night after night, which is wasted supply, which is wasted money. That's where they'd raise the price a few bucks to make up for the increased inventory.
And Disney's not being cheap, they're protecting their profit margins. Food thrown out is money lost.