A cryptocurrency that cost nothing to make will eventually worth nothing, because it is voluntarily participated. Why should I pay 200 dollar for something that cost nothing to make??? Suppose that you can generate 1 bitcoin today with a cost of 1 dollar, then everyone will immediately go to generate coin and sell it on market for $199 of profit right away, that will drag the price down to 1 dollar.
First, if I gave 144 people 25 bitcoins each, and they sold them, what would happen to the price of a bitcoin? According to you, the market would collapse because it cost them nothing to gain those bitcoins. Obviously, it wouldn't because there are enough free bitcoins to affect the market. You can't generate an unlimited number of bitcoins, so you can't drag the value down to the marginal cost.
Second, suppose Bitcoin was premined and 1 bitcoin was given to each of 21,000,000 people. Would the value of the bitcoins forever be 0? What if other people wanted some? What if people wanted two or more? What if one person managed to collect 10,000 and got someone to trade two pizzas for them? Would the value still forever be stuck at 0? No.
Don't you see? The value of a bitcoin has nothing to do with the cost of creating it. The supply of bitcoins does not depend on their value and bitcoins are not consumed. The economics of gold, oil, and other commodities do not apply to bitcoin.
These are good arguments
Your first assumption is exactly like those chinese miners with free electricity, they can dump their cheap coin on the market to make a quick buck. But since the bitcoin supply is extremely limited, a large hedge fund would still be possible to raise the market price by 10 fold regardless of sell pressure out there (They can anticipate how large the sell pressure can be)
However, after the rally is over, the hedge fund cashed out and went for vacation for two years, now we are left with all the miserable bitcoin investors seeing a falling market. In a falling market, many of bitcoin's promises are broken, so the demand will also shrink significantly. In such a time, how much should a bitcoin worth becomes very important for people's decision making. And naturally, a common indicator is the mining cost: If the coin worth more than mining cost, miners will sell, if lower, miners will hold, that will adjust the supply. And this is what happened during 2014, exchange rate kept going down until they got close to mining cost
And as you said, if there is no new supply, then even the cost is zero, the coin could still worth something if there is certain amount of demand. I'm not totally sure about this reasoning, but this reasoning can work if the demand of this coin is unique, can not be replaced by anything else(like diamond), or the demand is forced on many people (like fiat money). Bitcoin is not forced on anyone, so that leaves us with only the "unique demand" requirement, and there is indeed a unique demand: anti-inflation currency. Non of the other fiat currencies in the world are anti-inflation. However, any other cryptocurrency can also be anti-inflation
So what makes bitcoin different than any other alt-coins would be its large community. If this community is large enough, everyone prefer to use bitcoin for transaction, then bitcoin will work like fiat money, automatically hold its value without production cost. But to be honest, most of the community consists of speculators, real bitcoiners are minority, so the community and its value are very unstable, depends on the price movement
If there is any new coin generation, or fee generation, and people are possible to participate the mining, then the mining competition will raise its cost to the market price. Imagine that when one coin worth 1 million dollar while mining each block will give you a fee of 1 bitcoin, the mining cost of each block would get close to 1 million dollar due to competition
Actually you can also use this to explain the price rally: When this community expands very fast, the demand surge and the price of bitcoin will rise exponentially, causing the mining infrastructure to expand, mining cost to rise. And when price is going down, the community also shrinks very fast, the demand goes down and price crash further, but get some strong support around the mining cost