There isn't really unlimited demand. There's a concept called marginal utility developed by the early Austrian School of economics. The more you can get from a concrete good, the less you'll perceive a benefit from it.

Let's say McDonalds sets up a promo where you get 1 hamburger for $3, and then unlimited hamburgers for $0.50 each. How many hamburgers would you order? That shows that even if the original value of the good is $3 and you could get it for much less, you would have a limit where your marginal utility (the benefit of an additional burger) would fall under $0.50. Some would order 3-4 hamburgers because that's all they can eat at that time, others 10 because they store some in their fridge. But nobody would try to get a million.

For most goods there is indeed more demand than supply though. But humans normally allocate that quite fine with their own actions. If people want bread, someone will create a bakery and sell it to them. The government is only necessary if there is some imbalance somewhere. Some communist countries indeed wanted to delegate all that work to the government, but that has often failed because the process how markets work is extremely complex.