You are changing the meaning of words to make it sound like Bitcoin is something its not.
Intrinsic usually means value as a commodity independently of its value of money. that’s like the value of gold without the gold standard. The value of a monetised commodity is always greater than the intrinsic value because its use as money creates extra demand.
This also relates to your use of the word ‘back’. Backing refers to the commodity for which a paper receipt can be redeemed. you can sell bitcoin for dollars, you can burn bitcoin, but you can’t redeem them. Same as fiat money, they come ex nihilo and circulate in perpetuity.
The cost of production only drives the price of money when money is a commodity with intrinsic value. Bitcoin has no intrinsic value (although satoshis have some non-monetary uses) ergo, its price is not driven by the cost of production. I would argue on the contrary that the cost of production follows the price of bitcoin, because the higher the price, the more miners can be supported for it.
You neglect to mention that 97% of so-called fiat money is not issued ex-nihilo by the government but actually issued by banks as interest bearing debt. This money has very different qualities to the legal tender on which it is based.
Fiat money is not unlimited, but issued carefully by the government. Bank debt money is also limited by the bank’s risk appetite. All together it adds up to a growing shortage of money in the global economy.
I’m not sure what you mean by utility value. Does it count if I use a bank note to snort cocaine?
Maybe the real value of bitcoin is that it helps us to imagine a path to a better world. But that doesn’t make it a good currency in economic terms. In many ways, Bitcoin’s promise of decentralisation resonates with the promises of the early internet. Some of those promises are coming true over decades of social transformation, but other less foreseen things also preserve the balance of good and evil!